Voozh

WO N	👁 Image
👁 Image Palindromic Quasi_Over_Squares of the form n^2+(n+)
👁 rood n(n+0) 👁 rood n(n+1) 👁 rood n(n+2) 👁 rood n(n+) 👁 rood 👁 rood n^2+1 👁 rood n^2+ 👁 rood n^2– 👁 rood 👁 rood n^2+(n+1)

Introduction

Palindromic numbers are numbers which read the same from

👁 p_right
left to right (forwards) as from the right to left (backwards) 👁 p_left

Here are a few random examples : , ,

Quasi_Over_Square numbers are defined and calculated by this extraordinary intricate and excruciatingly complex formula.
So, this line is for experts only _{👁 Image}

PLAIN TEXT QUASIMOR

Palindromic Quasi_Over_Squares

Quasi_Over_Squares of the form x² + (x + 0) can only end with a , or . And if it terminates in , it terminates in or only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.

Main source see Palindromic Pronic Numbers

can be followed by any number : 20, 21, 22, 23, 24, 25, 26, 27, 28 or 29

can only be followed by 0 or 5 : 60 or 65

Quasi_Over_Squares of the form x² + (x + 1) can only end with a , or . And if it terminates in , it terminates in or only.
Even length palindromes of this form are not possible as never divisible by 11.

Main source see Palindromic Quasi-Over-Squares

can be followed by any number : 10, 11, 12, 13, 14, 15, 16, 17, 18 or 19

can be followed by any number : 30, 31, 32, 33, 34, 35, 36, 37, 38 or 39

can only be followed by 0 or 5 : 70 or 75

Quasi_Over_Squares of the form x² + (x + 2) can only end with a , or . And if it terminates in , it terminates in or only.

can be followed by any number : 20, 21, 22, 23, 24, 25, 26, 27, 28 or 29

can be followed by any number : 40, 41, 42, 43, 44, 45, 46, 47, 48 or 49

can only be followed by 0 or 5 : 80 or 85

👁 bu17
There are no palindromic Quasi_Over_Squares of type x^2 + (x+2) of lengths

Quasi_Over_Squares of the form x² + (x + 3) can only end with a , or . And if it terminates in , it terminates in or only.

can be followed by any number : 30, 31, 32, 33, 34, 35, 36, 37, 38 or 39

can be followed by any number : 50, 51, 52, 53, 54, 55, 56, 57, 58 or 59

can only be followed by 0 or 5 : or 95 { This ... produces ever expanding Mandelbrot-like infinite palindromes }.

👁 bu17
There are no palindromic Quasi_Over_Squares of type x^2 + (x+3) of lengths

Quasi_Over_Squares of the form x² + (x + 4) can only end with a , or . And if it terminates in , it terminates in or only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
Even length palindromes of this form are not possible as never divisible by 11.

can be followed by any number : 40, 41, 42, 43, 44, 45, 46, 47, 48 or 49

can be followed by any number : 60, 61, 62, 63, 64, 65, 66, 67, 68 or 69

👁 bu17
There are no palindromic Quasi_Over_Squares of type x^2 + (x+4) of EVEN length.

Quasi_Over_Squares of the form x² + (x + 5) can only end with a , or . And if it terminates in , it terminates in or only.

can only be followed by 1 or 6 : 11 or 16

can be followed by any number : 50, 51, 52, 53, 54, 55, 56, 57, 58 or 59

can be followed by any number : 70, 71, 72, 73, 74, 75, 76, 77, 78 or 79

👁 bu17
There are no palindromic Quasi_Over_Squares of type x^2 + (x+5) of lengths

Quasi_Over_Squares of the form x² + (x + 6) can only end with a , or . And if it terminates in , it terminates in or only.
Even length palindromes of this form are not possible as never divisible by 11.

can only be followed by 1 or 6 : 21 or 26

can be followed by any number : 60, 61, 62, 63, 64, 65, 66, 67, 68 or 69

can be followed by any number : 80, 81, 82, 83, 84, 85, 86, 87, 88 or 89

👁 bu17
There are no palindromic Quasi_Over_Squares of type x^2 + (x+6) of EVEN length nor of length

Quasi_Over_Squares of the form x² + (x + 7) can only end with a , or . And if it terminates in , it terminates in or only.
Even length palindromes of this form are not possible as never divisible by 11.

can only be followed by 1 or 6 : 31 or 36

can be followed by any number : 70, 71, 72, 73, 74, 75, 76, 77, 78 or 79

can be followed by any number : 90, 91, 92, 93, 94, 95, 96, 97, 98 or 99

👁 bu17
There are no palindromic Quasi_Over_Squares of type x^2 + (x+7) of EVEN length.

Quasi_Over_Squares of the form x² + (x + 8) can only end with a , or . And if it terminates in , it terminates in or only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
Even length palindromes of this form are not possible as never divisible by 11.

can only be followed by 1 or 6 : 41 or 46

can be followed by any number : 80, 81, 82, 83, 84, 85, 86, 87, 88 or 89

👁 bu17
There are no palindromic Quasi_Over_Squares of type x^2 + (x+8) of EVEN length nor of lengths

Quasi_Over_Squares of the form x² + (x + 9) can only end with a , or . And if it terminates in , it terminates in or only.

can be followed by any number : 10, 11, 12, 13, 14, 15, 16, 17, 18 or 19

can only be followed by 1 or 6 : 51 or 56

can be followed by any number : 90, 91, 92, 93, 94, 95, 96, 97, 98 or 99

👁 bu17
There are no palindromic Quasi_Over_Squares of type x^2 + (x+9) of lengths

Quasi_Over_Squares	Change of variables	CUDApalin parameters	Base Correction
x^2 + (x+0)	n.a.		base = CUDAbase
x^2 + (x+1)	n.a.		base = CUDAbase
x^2 + (x+2)	n.a.		base = CUDAbase
x^2 + (x+3)	n.a.		base = CUDAbase
x^2 + (x+4)	n.a.		base = CUDAbase
x^2 + (x+5)	n.a.		base = CUDAbase
x^2 + (x+6)	n.a.		base = CUDAbase
x^2 + (x+7)	n.a.		base = CUDAbase
x^2 + (x+8)	n.a.		base = CUDAbase
x^2 + (x+9)	n.a.		base = CUDAbase

Some people regard as a bad year !

So does because he figured out that after applying the procedure to ,

this yearnumber never transformed into a palindrome. Follow this link to arrive at his website.

1997: A Bad Year

As for me, is a lucky year because of the following relations with the number of the beast and other various palindromic numbers :

+ ( + 9 ) = or from the right .

Note that = +

+ ( + ) = .

Note that = +

and moreover = is a palindromic cube !

An palindromic pattern resides in the list for

Some palindromic pattern resides in the list for

An palindromic pattern hides in the list for

A very nice but palindromic pattern hides in the list for

is no longer palindromic !

An palindromic pattern hides in the list for

A second peculiar palindromic pattern emerges as well.

An palindromic pattern hides in the list for

The Table

Index Nr		Length
Index Nr		Length
👁 up	👁 down
👁 up	👁 down	[Scanned exhaustively up to length 59]
👁 up	👁 down
👁 up	👁 down	[Scanned exhaustively up to length 57]
👁 up	👁 down
👁 up	👁 down	One can find the regular numbers of the form n+(n+2) at %N under A014206. The palindromic numbers of the form n+(n+2) are categorised as follows : %N under A027712. %N under A027713. More terms from , Aug 28, 2018. See Index Nrs 51 up to 65. More terms from , Sep 1, 2020. See Index Nrs 66 up to 115. More terms from , Nov 3, 2022. See Index Nrs 116 up to 121. More terms from , Nov 11, 2022. See Index Nrs 122 up to 128. More terms from , Dec 6, 2022. See Index Nrs 129 up to 152. More terms from , Jun 21, 2023. See Index Nrs 153 up to 155. More terms from , Jul 18, 2023. See Index Nrs 156 up to 161.
161	28
161	55
160	28
160	55
159	28
159	55
158	28
158	55
157	28
157	55
156	28
156	55
155	27
155	53
154	27
154	53
153	27
153	53
152	27
152	53
151	26
151	51
150	26
150	51
149	26
149	51
148	25
148	50
147	25
147	49
146	25
146	49
145	25
145	49
144	25
144	49
143	25
143	49
142	25
142	49
141	25
141	49
140	25
140	49
139	25
139	49
138	24
138	47
137	24
137	47
136	24
136	47
135	24
135	47
134	23
134	46
133	23
133	46
132	23
132	46
131	23
131	45
130	23
130	45
129	23
129	45
128	22
128	44
127	22
127	44
126	22
126	43
125	22
125	43
124	22
124	43
123	21
123	42
122	21
122	42
121	21
121	41
120	21
120	41
119	21
119	41
118	21
118	41
117	20
117	40
116	20
116	40
115	20
115	39
114	20
114	39
113	20
113	39
112	20
112	39
111	20
111	39
110	20
110	39
109	20
109	39
108	19
108	37
107	19
107	37
106	19
106	37
105	19
105	37
104	19
104	37
103	18
103	36
102	18
102	36
101	18
101	36
100	18
100	35
99	17
99	33
98	17
98	33
97	16
97	32
96	16
96	32
95	16
95	31
94	16
94	31
93	16
93	31
92	16
92	31
91	16
91	31
90	16
90	31
89	16
89	31
88	16
88	31
87	15
87	30
86	15
86	29
85	15
85	29
84	15
84	29
83	14
83	27
82	14
82	27
81	13
81	26
80	13
80	26
79	13
79	25
78	13
78	25
77	13
77	25
76	13
76	25
75	13
75	25
74	13
74	25
73	13
73	25
72	13
72	25
71	13
71	25
70	13
70	25
69	12
69	24
68	12
68	24
67	12
67	24
66	12
66	24
65	12
65	24
64	12
64	23
63	12
63	23
62	11
62	22
61	11
61	22
60	11
60	22
59	11
59	22
58	11
58	21
57	10
57	20
56	10
56	19
55	10
55	19
54	10
54	19
53	10
53	19
52	10
52	19
51	10
51	19
50	10
50	19
49	10
49	19
48	10
48	19
47	9
47	18
46	9
46	18
45	9
45	17
44	9
44	17
43	9
43	17
42	9
42	17
41	8
41	16
40	8
40	16
39	8
39	15
38	8
38	15
37	8
37	15
36	8
36	15
35	8
35	15
34	8
34	15
33	8
33	15
32	7
32	13
31	7
31	13
30	7
30	13
29	6
29	12
28	6
28	11
27	6
27	11
26	5
26	10
25	5
25	9
24	5
24	9
23	5
23	9
22	5
22	9
21	4
21	7
20	4
20	7
19	4
19	7
18	4
18	7
17	4
17	7
16	4
16	7
15	3
15	6
14	3
14	6
13	3
13	5
12	3
12	5
11	3
11	5
10	2
10	4
9	2
9	4
8	2
8	3
7	2
7	3
6	2
6	3
5	1
5	2
4	1
4	2
3	1
3	1
2	1
2	1
1	1
1	1
👁 up	👁 down
👁 up	👁 down	One can find the regular numbers of the form n+(n+3) at %N under A027688. The palindromic numbers of the form n+(n+3) are categorised as follows : %N under A027714. %N under A027715. More terms from , Aug 29, 2018. See Index Nrs 38 up to 50. More terms from , Sep 1, 2020. See Index Nrs 51 up to 124. More terms from , Nov 11, 2022. See Index Nrs 126 up to 188 except Nr 167 which was already known. More terms from , Dec 6, 2022. See Index Nrs 189 up to 316 except Nr 286 which was already known. More terms from , Jun 22, 2023. See Index Nrs 317 up to 352 More terms from , Jul 18, 2023. See Index Nrs 353 up to 392

392	28
392	55
391	28
391	55
390	28
390	55
389	28
389	55
388	28
388	55
387	28
387	55
386	28
386	55
385	28
385	55
384	28
384	55
383	28
383	55
382	28
382	55
381	28
381	55
380	28
380	55
379	28
379	55
378	28
378	55
377	28
377	55
376	28
376	55
375	28
375	55
374	28
374	55
373	28
373	55
372	28
372	55
371	28
371	55
370	28
370	55
369	28
369	55
368	28
368	55
367	28
367	55
366	28
366	55
365	28
365	55
364	28
364	55
363	28
363	55
362	28
362	55
361	28
361	55
360	28
360	55
359	28
359	55
358	28
358	55
357	28
357	55
356	28
356	55
355	28
355	55
354	28
354	55
353	28
353	55
352	27
352	53
351	27
351	53
350	27
350	53
349	27
349	53
348	27
348	53
347	27
347	53
346	27
346	53
345	27
345	53
344	27
344	53
343	27
343	53
342	27
342	53
341	27
341	53
340	27
340	53
339	27
339	53
338	27
338	53
337	27
337	53
336	27
336	53
335	27
335	53
334	27
334	53
333	27
333	53
332	27
332	53
331	27
331	53
330	27
330	53
329	27
329	53
328	27
328	53
327	27
327	53
326	27
326	53
325	27
325	53
324	27
324	53
323	27
323	53
322	27
322	53
321	27
321	53
320	27
320	53
319	27
319	53
318	27
318	53
317	27
317	53
316	26
316	51
315	26
315	51
314	26
314	51
313	26
313	51
312	26
312	51
311	26
311	51
310	26
310	51
309	26
309	51
308	26
308	51
307	26
307	51
306	26
306	51
305	26
305	51
304	26
304	51
303	26
303	51
302	26
302	51
301	26
301	51
300	26
300	51
299	26
299	51
298	26
298	51
297	26
297	51
296	26
296	51
295	26
295	51
294	26
294	51
293	26
293	51
292	26
292	51
291	26
291	51
290	26
290	51
289	26
289	51
288	26
288	51
287	26
287	51
286	26
286	51
285	26
285	51
284	26
284	51
283	26
283	51
282	26
282	51
281	25
281	50
280	25
280	50
279	25
279	49
278	25
278	49
277	25
277	49
276	25
276	49
275	25
275	49
274	25
274	49
273	25
273	49
272	25
272	49
271	25
271	49
270	25
270	49
269	25
269	49
268	25
268	49
267	25
267	49
266	25
266	49
265	25
265	49
264	25
264	49
263	25
263	49
262	25
262	49
261	25
261	49
260	25
260	49
259	25
259	49
258	25
258	49
257	25
257	49
256	25
256	49
255	25
255	49
254	25
254	49
253	25
253	49
252	25
252	49
251	25
251	49
250	25
250	49
249	25
249	49
248	25
248	49
247	25
247	49
246	25
246	49
245	25
245	49
244	24
244	48
243	24
243	47
242	24
242	47
241	24
241	47
240	24
240	47
239	24
239	47
238	24
238	47
237	24
237	47
236	24
236	47
235	24
235	47
234	24
234	47
233	24
233	47
232	24
232	47
231	24
231	47
230	24
230	47
229	24
229	47
228	24
228	47
227	24
227	47
226	24
226	47
225	24
225	47
224	24
224	47
223	24
223	47
222	24
222	47
221	24
221	47
220	24
220	47
219	24
219	47
218	23
218	46
217	23
217	46
216	23
216	46
215	23
215	45
214	23
214	45
213	23
213	45
212	23
212	45
211	23
211	45
210	23
210	45
209	23
209	45
208	23
208	45
207	23
207	45
206	23
206	45
205	23
205	45
204	23
204	45
203	23
203	45
202	23
202	45
201	23
201	45
200	23
200	45
199	23
199	45
198	23
198	45
197	23
197	45
196	23
196	45
195	23
195	45
194	23
194	45
193	23
193	45
192	23
192	45
191	23
191	45
190	23
190	45
189	23
189	45
188	22
188	43
187	22
187	43
186	22
186	43
185	22
185	43
184	22
184	43
183	22
183	43
182	22
182	43
181	22
181	43
180	22
180	43
179	22
179	43
178	22
178	43
177	22
177	43
176	22
176	43
175	22
175	43
174	22
174	43
173	22
173	43
172	22
172	43
171	22
171	43
170	22
170	43
169	22
169	43
168	22
168	43
167	22
167	43
166	22
166	43
165	22
165	43
164	22
164	43
163	22
163	43
162	22
162	43
161	21
161	42
160	21
160	41
159	21
159	41
158	21
158	41
157	21
157	41
156	21
156	41
155	21
155	41
154	21
154	41
153	21
153	41
152	21
152	41
151	21
151	41
150	21
150	41
149	21
149	41
148	21
148	41
147	21
147	41
146	21
146	41
145	21
145	41
144	21
144	41
143	21
143	41
142	21
142	41
141	21
141	41
140	20
140	40
139	20
139	39
138	20
138	39
137	20
137	39
136	20
136	39
135	20
135	39
134	20
134	39
133	20
133	39
132	20
132	39
131	20
131	39
130	20
130	39
129	20
129	39
128	20
128	39
127	20
127	39
126	20
126	39
125	19
125	38
124	19
124	37
123	19
123	37
122	19
122	37
121	19
121	37
120	19
120	37
119	19
119	37
118	19
118	37
117	19
117	37
116	19
116	37
115	19
115	37
114	19
114	37
113	19
113	37
112	19
112	37
111	19
111	37
110	18
110	35
109	18
109	35
108	18
108	35
107	18
107	35
106	18
106	35
105	18
105	35
104	18
104	35
103	18
103	35
102	18
102	35
101	18
101	35
100	17
100	33
99	17
99	33
98	17
98	33
97	17
97	33
96	17
96	33
95	17
95	33
94	17
94	33
93	17
93	33
92	17
92	33
91	17
91	33
90	17
90	33
89	17
89	33
88	17
88	33
87	16
87	31
86	16
86	31
85	16
85	31
84	16
84	31
83	16
83	31
82	16
82	31
81	16
81	31
80	16
80	31
79	16
79	31
78	16
78	31
77	15
77	29
76	15
76	29
75	15
75	29
74	15
74	29
73	15
73	29
72	15
72	29
71	15
71	29
70	15
70	29
69	15
69	29
68	15
68	29
67	14
67	27
66	14
66	27
65	14
65	27
64	14
64	27
63	14
63	27
62	14
62	27
61	14
61	27
60	14
60	27
59	13
59	26
58	13
58	25
57	13
57	25
56	13
56	25
55	13
55	25
54	13
54	25
53	13
53	25
52	13
52	25
51	13
51	25
50	13
50	25
49	12
49	23
48	12
48	23
47	12
47	23
46	11
46	22
45	11
45	22
44	11
44	21
43	11
43	21
42	11
42	21
41	10
41	19
40	10
40	19
39	10
39	19
38	10
38	19
37	10
37	19
36	9
36	18
35	9
35	18
34	9
34	18
33	9
33	18
32	9
32	17
31	9
31	17
30	9
30	17
29	8
29	16
28	8
28	16
27	8
27	15
26	8
26	15
25	8
25	15
24	7
24	14
23	7
23	13
22	6
22	12
21	6
21	11
20	6
20	11
19	5
19	10
18	5
18	10
17	5
17	9
16	5
16	9
15	4
15	8
14	4
14	7
13	3
13	6
12	3
12	5
11	3
11	5
10	3
10	5
9	3
9	5
8	2
8	4
7	2
7	4
6	2
6	3
5	2
5	3
4	1
4	2
3	1
3	1
2	1
2	1
1	1
1	1

👁 up	👁 down
👁 up	👁 down	One can find the regular numbers of the form n+(n+4) at %N under A027689. The palindromic numbers of the form n+(n+4) are categorised as follows : %N under A027716. %N under A027717. More terms from , Aug 29, 2018. See Index Nrs 33 up to 36. More terms from , Sep 1, 2020. See Index Nrs 37 up to 57. More terms from , Nov 11, 2022. See Index Nrs 58 up to 70. More terms from , Dec 6, 2022. See Index Nrs 71 up to 77. More terms from , Jun 22, 2023. See Index Nrs 78 up to 81. More terms from , Jul 18, 2023. See Index Nr 82.
82	28
82	55
81	27
81	53
80	27
80	53
79	27
79	53
78	27
78	53
77	26
77	51
76	25
76	49
75	25
75	49
74	24
74	47
73	24
73	47
72	23
72	45
71	23
71	45
70	22
70	43
69	22
69	43
68	21
68	41
67	21
67	41
66	21
66	41
65	21
65	41
64	21
64	41
63	20
63	39
62	20
62	39
61	20
61	39
60	20
60	39
59	20
59	39
58	20
58	39
57	19
57	37
56	19
56	37
55	19
55	37
54	18
54	35
53	18
53	35
52	17
52	33
51	17
51	33
50	16
50	31
49	16
49	31
48	16
48	31
47	16
47	31
46	15
46	29
45	15
45	29
44	15
44	29
43	15
43	29
42	14
42	27
41	14
41	27
40	14
40	27
39	14
39	27
38	14
38	27
37	14
37	27
36	13
36	25
35	13
35	25
34	13
34	25
33	13
33	25
32	12
32	23
31	11
31	21
30	11
30	21
29	11
29	21
28	11
28	21
27	11
27	21
26	10
26	19
25	10
25	19
24	9
24	17
23	9
23	17
22	8
22	15
21	8
21	15
20	7
20	13
19	7
19	13
18	7
18	13
17	7
17	13
16	6
16	11
15	6
15	11
14	6
14	11
13	6
13	11
12	5
12	9
11	5
11	9
10	4
10	7
9	4
9	7
8	4
8	7
7	4
7	7
6	3
6	5
5	3
5	5
4	3
4	5
3	2
3	3
2	1
2	1
1	1
1	1
👁 up	👁 down
👁 up	👁 down	One can find the regular numbers of the form n+(n+5) at %N under A027690. The palindromic numbers of the form n+(n+5) are categorised as follows : %N under A027718. %N under A027728. More terms from , Aug 28, 2018. See Index Nrs 30 up to 46. More terms from , Sep 1, 2020. See Index Nrs 47 up to 79. More terms from , Nov 11, 2022. See Index Nrs 80 up to 87. More terms from , Dec 6, 2022. See Index Nrs 88 up to 94. More terms from , Jul 18, 2023. See Index Nrs 95 up to 97.
97	28
97	55
96	28
96	55
95	28
95	55
94	25
94	50
93	25
93	50
92	24
92	47
91	24
91	47
90	23
90	46
89	23
89	45
88	23
88	45
87	22
87	44
86	22
86	43
85	22
85	43
84	22
84	43
83	22
83	43
82	21
82	41
81	21
81	41
80	20
80	39
79	19
79	38
78	19
78	37
77	19
77	37
76	19
76	37
75	19
75	37
74	19
74	37
73	19
73	37
72	18
72	36
71	18
71	36
70	18
70	35
69	18
69	35
68	18
68	35
67	18
67	35
66	17
66	34
65	17
65	33
64	17
64	33
63	17
63	33
62	17
62	33
61	16
61	32
60	16
60	32
59	16
59	31
58	16
58	31
57	16
57	31
56	16
56	31
55	15
55	30
54	15
54	29
53	15
53	29
52	15
52	29
51	15
51	29
50	15
50	29
49	15
49	29
48	15
48	29
47	14
47	27
46	13
46	25
45	13
45	25
44	13
44	25
43	13
43	25
42	12
42	24
41	12
41	23
40	12
40	23
39	11
39	22
38	11
38	22
37	11
37	21
36	11
36	21
35	11
35	21
34	10
34	20
33	10
33	19
32	10
32	19
31	10
31	19
30	10
30	19
29	10
29	19
28	9
28	17
27	8
27	16
26	8
26	16
25	7
25	14
24	7
24	14
23	7
23	13
22	7
22	13
21	7
21	13
20	6
20	11
19	6
19	11
18	5
18	9
17	5
17	9
16	5
16	9
15	5
15	9
14	4
14	8
13	4
13	8
12	4
12	8
11	4
11	7
10	3
10	5
9	3
9	5
8	3
8	5
7	2
7	4
6	2
6	3
5	2
5	3
4	1
4	2
3	1
3	2
2	1
2	1
1	1
1	1
👁 up	👁 down
👁 up	👁 down	One can find the regular numbers of the form n+(n+6) at %N under A027691. The palindromic numbers of the form n+(n+6) are categorised as follows : %N under A027729. %N under A027721. More terms from , Aug 27, 2018. See Index Nrs 32 up to 34. More terms from , Sep 1, 2020. See Index Nrs 35 up to 54. More terms from , Nov 11, 2022. See Index Nrs 55 up to 63. More terms from , Dec 6, 2022. See Index Nrs 64 up to 75. More terms from , Jun 22, 2023. See Index Nrs 76 up to 78. More terms from , Jul 18, 2023. See Index Nr 79.
79	28
79	55
78	27
78	53
77	27
77	53
76	27
76	53
75	26
75	51
74	26
74	51
73	26
73	51
72	26
72	51
71	25
71	49
70	25
70	49
69	25
69	49
68	25
68	49
67	24
67	47
66	24
66	47
65	24
65	47
64	23
64	45
63	22
63	43
62	22
62	43
61	21
61	41
60	21
60	41
59	21
59	41
58	21
58	41
57	21
57	41
56	21
56	41
55	20
55	39
54	19
54	37
53	19
53	37
52	19
52	37
51	19
51	37
50	18
50	35
49	18
49	35
48	18
48	35
47	17
47	33
46	17
46	33
45	15
45	29
44	15
44	29
43	15
43	29
42	14
42	27
41	13
41	25
40	13
40	25
39	13
39	25
38	13
38	25
37	13
37	25
36	12
36	23
35	12
35	23
34	11
34	21
33	11
33	21
32	10
32	19
31	10
31	19
30	9
30	17
29	9
29	17
28	9
28	17
27	8
27	15
26	8
26	15
25	8
25	15
24	8
24	15
23	8
23	15
22	7
22	13
21	7
21	13
20	7
20	13
19	7
19	13
18	7
18	13
17	7
17	13
16	7
16	13
15	6
15	11
14	6
14	11
13	6
13	11
12	6
12	11
11	5
11	9
10	4
10	7
9	4
9	7
8	4
8	7
7	4
7	7
6	3
6	5
5	2
5	3
4	2
4	3
3	2
3	3
2	1
2	1
1	1
1	1
👁 up	👁 down
👁 up	👁 down	One can find the regular numbers of the form n+(n+7) at %N under A027692. The palindromic numbers of the form n+(n+7) are categorised as follows : %N under A027722. %N under A027723. More terms from , Aug 28, 2018. See Index Nrs 28 up to 45. More terms from , Sep 1, 2020. See Index Nrs 46 up to 71. More terms from , Nov 11, 2022. See Index Nrs 72 up to 80. More terms from , Dec 6, 2022. See Index Nrs 81 up to 96. More terms from , Jun 22, 2023. See Index Nrs 97 up to 99. More terms from , Jul 18, 2023. See Index Nrs 100 up to 103.
103	28
103	55
102	28
102	55
101	28
101	55
100	28
100	55
99	27
99	53
98	27
98	53
97	27
97	53
96	26
96	51
95	26
95	51
94	25
94	49
93	25
93	49
92	25
92	49
91	25
91	49
90	25
90	49
89	25
89	49
88	24
88	47
87	24
87	47
86	24
86	47
85	24
85	47
84	23
84	45
83	23
83	45
82	23
82	45
81	23
81	45
80	22
80	43
79	22
79	43
78	21
78	41
77	21
77	41
76	20
76	39
75	20
75	39
74	20
74	39
73	20
73	39
72	20
72	39
71	19
71	37
70	19
70	37
69	19
69	37
68	19
68	37
67	19
67	37
66	18
66	35
65	18
65	35
64	18
64	35
63	18
63	35
62	17
62	33
61	17
61	33
60	17
60	33
59	17
59	33
58	16
58	31
57	16
57	31
56	16
56	31
55	16
55	31
54	16
54	31
53	15
53	29
52	15
52	29
51	15
51	29
50	15
50	29
49	15
49	29
48	14
48	27
47	14
47	27
46	14
46	27
45	13
45	25
44	13
44	25
43	13
43	25
42	13
42	25
41	13
41	25
40	13
40	25
39	12
39	23
38	12
38	23
37	12
37	23
36	12
36	23
35	12
35	23
34	11
34	21
33	11
33	21
32	11
32	21
31	11
31	21
30	11
30	21
29	11
29	21
28	10
28	19
27	10
27	19
26	10
26	19
25	10
25	19
24	9
24	17
23	9
23	17
22	8
22	15
21	8
21	15
20	8
20	15
19	7
19	13
18	7
18	13
17	6
17	11
16	6
16	11
15	6
15	11
14	5
14	9
13	5
13	9
12	4
12	7
11	4
11	7
10	4
10	7
9	3
9	5
8	3
8	5
7	3
7	5
6	3
6	5
5	3
5	5
4	2
4	3
3	2
3	3
2	1
2	1
1	1
1	1
👁 up	👁 down
👁 up	👁 down	One can find the regular numbers of the form n+(n+8) at %N under A027693. The palindromic numbers of the form n+(n+8) are categorised as follows : %N under A027724. %N under A027725. More terms from , Aug 29, 2018. See Index Nrs 16 up to 19. More terms from , Sep 1, 2020. See Index Nrs 20 up to 32. More terms from , Nov 11, 2022. See Index Nrs 33 up to 41. More terms from , Dec 6, 2022. See Index Nrs 42 up to 45. More terms from , Jun 22, 2023. See Index Nr 46. More terms from , Jul 18, 2023. See Index Nr 47.
47	28
47	55
46	27
46	53
45	26
45	51
44	26
44	51
43	25
43	49
42	25
42	49
41	22
41	43
40	22
40	43
39	22
39	43
38	21
38	41
37	20
37	39
36	20
36	39
35	20
35	39
34	20
34	39
33	20
33	39
32	19
32	37
31	19
31	37
30	18
30	35
29	17
29	33
28	17
28	33
27	17
27	33
26	17
26	33
25	16
25	31
24	16
24	31
23	16
23	31
22	16
22	31
21	15
21	29
20	15
20	29
19	14
19	27
18	14
18	27
17	12
17	23
16	12
16	23
15	10
15	19
14	9
14	17
13	7
13	13
12	7
12	13
11	7
11	13
10	7
10	13
9	6
9	11
8	5
8	9
7	5
7	9
6	4
6	7
5	4
5	7
4	3
4	5
3	3
3	5
2	2
2	3
1	1
1	1
👁 up	👁 down
👁 up	👁 down	One can find the regular numbers of the form n+(n+9) at %N under A027694. The palindromic numbers of the form n+(n+9) are categorised as follows : %N under A027726. %N under A027727. More terms from , Aug 29, 2018. From Index Nrs 64 up to 71. More terms from , Sep 1, 2020. See Index Nrs 72 up to 117. More terms from , Nov 11, 2022. See Index Nrs 118 up to 139. More terms from , Dec 6, 2022. See Index Nrs 140 up to 164. More terms from , Jun 22, 2023. See Index Nr 165. More terms from , Jul 18, 2023. See Index Nrs 166 up to 170.
170	28
170	55
169	28
169	55
168	28
168	55
167	28
167	55
166	27
166	54
165	27
165	53
164	26
164	52
163	26
163	51
162	26
162	51
161	26
161	51
160	26
160	51
159	26
159	51
158	25
158	50
157	25
157	50
156	25
156	50
155	25
155	49
154	25
154	49
153	25
153	49
152	25
152	49
151	25
151	49
150	24
150	48
149	24
149	47
148	24
148	47
147	24
147	47
146	24
146	47
145	24
145	47
144	23
144	46
143	23
143	46
142	23
142	46
141	23
141	45
140	23
140	45
139	22
139	44
138	22
138	44
137	22
137	43
136	22
136	43
135	22
135	43
134	22
134	43
133	22
133	43
132	22
132	43
131	21
131	42
130	21
130	42
129	21
129	41
128	21
128	41
127	21
127	41
126	21
126	41
125	21
125	41
124	20
124	40
123	20
123	39
122	20
122	39
121	20
121	39
120	20
120	39
119	20
119	39
118	20
118	39
117	19
117	38
116	19
116	38
115	19
115	38
114	19
114	37
113	19
113	37
112	19
112	37
111	19
111	37
110	19
110	37
109	19
109	37
108	19
108	37
107	19
107	37
106	18
106	36
105	18
105	36
104	18
104	35
103	18
103	35
102	18
102	35
101	17
101	33
100	17
100	33
99	17
99	33
98	17
98	33
97	17
97	33
96	17
96	33
95	16
95	32
94	16
94	31
93	16
93	31
92	16
92	31
91	16
91	31
90	16
90	31
89	15
89	30
88	15
88	30
87	15
87	29
86	15
86	29
85	15
85	29
84	14
84	28
83	14
83	28
82	14
82	27
81	14
81	27
80	14
80	27
79	14
79	27
78	14
78	27
77	13
77	26
76	13
76	25
75	13
75	25
74	13
74	25
73	13
73	25
72	12
72	24
71	12
71	23
70	12
70	23
69	12
69	23
68	12
68	23
67	11
67	21
66	11
66	21
65	11
65	21
64	10
64	19
63	10
63	19
62	10
62	19
61	9
61	18
60	9
60	18
59	9
59	18
58	9
58	18
57	9
57	18
56	9
56	17
55	9
55	17
54	9
54	17
53	9
53	17
52	9
52	17
51	8
51	16
50	8
50	16
49	8
49	16
48	8
48	15
47	8
47	15
46	8
46	15
45	8
45	15
44	8
44	15
43	8
43	15
42	8
42	15
41	7
41	14
40	7
40	14
39	7
39	13
38	7
38	13
37	7
37	13
36	7
36	13
35	7
35	13
34	6
34	12
33	6
33	12
32	6
32	12
31	6
31	11
30	6
30	11
29	6
29	11
28	6
28	11
27	6
27	11
26	6
26	11
25	5
25	10
24	5
24	9
23	5
23	9
22	4
22	8
21	4
21	8
20	4
20	7
19	4
19	7
18	4
18	7
17	4
17	7
16	4
16	7
15	3
15	6
14	3
14	6
13	3
13	6
12	3
12	5
11	3
11	5
10	3
10	5
9	3
9	5
8	2
8	4
7	2
7	3
6	2
6	3
5	2
5	3
4	2
4	3
3	1
3	2
2	1
2	2
1	1
1	1

Sources Revealed

's Encyclopedia can be consulted online :

Neil Sloane's Integer Sequences

If you are interested in the of these numbers rather than the palindromes,
well look no further :

%N under A002384

%N under A002383

%N under A027752

%N under A027753

%N under A027754

%N under A027755

%N under A027756

%N or under A005471

%N under A027757

%N under A027758

Two more formula's are included in the table. They are well known to prime-lovers.

n + n + 17 generates 16 primes for all n values 0 to 15 !

%N under A028823

%N under A007636

%N under A007635

n + n + 41 generates 40 primes for all n values 0 to 39 !

%N under A002837

%N under A007634

%N under A005846

Click here to view some of the author's [] entries to the table.
Click here to view some entries to the table about palindromes.

Contributions

Copy & pasted from the OEIS Encyclopedia many more results from as indicated in the headings.

[ ]
Contribution from (email)

“ I'm still working on some upgrades to the program, but in the meantime, I thought I'd share
the length-40 and length-41 entries for Case X = 2 [n^2 + n + 2] found by my program:

[ See entries [] up to [] in the table.]

Length-40 took 229 seconds and length-41 took 689 seconds on my machine to generate.

Best,
Robert.”

[ ]
(email) added

for Case X = 2 [n^2 + n + 2] entries [] up to [].

for Case X = 3 [n^2 + n + 3] entries [] up to [], except entry [] which was already known.

for Case X = 4 [n^2 + n + 4] entries [] up to [].

for Case X = 5 [n^2 + n + 5] entries [] up to [].

for Case X = 6 [n^2 + n + 6] entries [] up to [].

for Case X = 7 [n^2 + n + 7] entries [] up to [].

for Case X = 8 [n^2 + n + 8] entries [] up to [].

for Case X = 9 [n^2 + n + 9] entries [] up to [].

[ ]
(email) added

for Case X = 2 [n^2 + n + 2] entries [] up to [].

for Case X = 3 [n^2 + n + 3] entries [] up to [], except entry [] which was already known.

for Case X = 4 [n^2 + n + 4] entries [] up to [].

for Case X = 5 [n^2 + n + 5] entries [] up to [].

for Case X = 6 [n^2 + n + 6] entries [] up to [].

for Case X = 7 [n^2 + n + 7] entries [] up to [].

for Case X = 8 [n^2 + n + 8] entries [] up to [].

for Case X = 9 [n^2 + n + 9] entries [] up to [].

[ ]
(email) added

for Case X = 2 [n^2 + n + 2] entries [] up to [].

for Case X = 3 [n^2 + n + 3] entries [] up to [].

for Case X = 4 [n^2 + n + 4] entries [] up to [].

for Case X = 6 [n^2 + n + 6] entries [] up to [].

for Case X = 7 [n^2 + n + 7] entries [] up to [].

for Case X = 8 [n^2 + n + 8] entry [].

for Case X = 9 [n^2 + n + 9] entry [].

[ ]
(email) added

for Case X = 2 [n^2 + n + 2] entries [] up to [].

for Case X = 3 [n^2 + n + 3] entries [] up to [].

for Case X = 4 [n^2 + n + 4] entry [].

for Case X = 5 [n^2 + n + 5] entries [] up to [].

for Case X = 6 [n^2 + n + 6] entry [].

for Case X = 7 [n^2 + n + 7] entries [] up to [].

for Case X = 8 [n^2 + n + 8] entry [].

for Case X = 9 [n^2 + n + 9] entry [] up to [].

[👁 up
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- Last modified : October 7, 2024.

Patrick De Geest - Belgium 👁 flag
- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com

URL: https://www.worldofnumbers.com/quasimor.htm

⇱ Palindromic Quasi_Over_Squares of the form n^2+(n+X)

392	28
392	55
391	28
391	55
390	28
390	55
389	28
389	55
388	28
388	55
387	28
387	55
386	28
386	55
385	28
385	55
384	28
384	55
383	28
383	55
382	28
382	55
381	28
381	55
380	28
380	55
379	28
379	55
378	28
378	55
377	28
377	55
376	28
376	55
375	28
375	55
374	28
374	55
373	28
373	55
372	28
372	55
371	28
371	55
370	28
370	55
369	28
369	55
368	28
368	55
367	28
367	55
366	28
366	55
365	28
365	55
364	28
364	55
363	28
363	55
362	28
362	55
361	28
361	55
360	28
360	55
359	28
359	55
358	28
358	55
357	28
357	55
356	28
356	55
355	28
355	55
354	28
354	55
353	28
353	55
352	27
352	53
351	27
351	53
350	27
350	53
349	27
349	53
348	27
348	53
347	27
347	53
346	27
346	53
345	27
345	53
344	27
344	53
343	27
343	53
342	27
342	53
341	27
341	53
340	27
340	53
339	27
339	53
338	27
338	53
337	27
337	53
336	27
336	53
335	27
335	53
334	27
334	53
333	27
333	53
332	27
332	53
331	27
331	53
330	27
330	53
329	27
329	53
328	27
328	53
327	27
327	53
326	27
326	53
325	27
325	53
324	27
324	53
323	27
323	53
322	27
322	53
321	27
321	53
320	27
320	53
319	27
319	53
318	27
318	53
317	27
317	53
316	26
316	51
315	26
315	51
314	26
314	51
313	26
313	51
312	26
312	51
311	26
311	51
310	26
310	51
309	26
309	51
308	26
308	51
307	26
307	51
306	26
306	51
305	26
305	51
304	26
304	51
303	26
303	51
302	26
302	51
301	26
301	51
300	26
300	51
299	26
299	51
298	26
298	51
297	26
297	51
296	26
296	51
295	26
295	51
294	26
294	51
293	26
293	51
292	26
292	51
291	26
291	51
290	26
290	51
289	26
289	51
288	26
288	51
287	26
287	51
286	26
286	51
285	26
285	51
284	26
284	51
283	26
283	51
282	26
282	51
281	25
281	50
280	25
280	50
279	25
279	49
278	25
278	49
277	25
277	49
276	25
276	49
275	25
275	49
274	25
274	49
273	25
273	49
272	25
272	49
271	25
271	49
270	25
270	49
269	25
269	49
268	25
268	49
267	25
267	49
266	25
266	49
265	25
265	49
264	25
264	49
263	25
263	49
262	25
262	49
261	25
261	49
260	25
260	49
259	25
259	49
258	25
258	49
257	25
257	49
256	25
256	49
255	25
255	49
254	25
254	49
253	25
253	49
252	25
252	49
251	25
251	49
250	25
250	49
249	25
249	49
248	25
248	49
247	25
247	49
246	25
246	49
245	25
245	49
244	24
244	48
243	24
243	47
242	24
242	47
241	24
241	47
240	24
240	47
239	24
239	47
238	24
238	47
237	24
237	47
236	24
236	47
235	24
235	47
234	24
234	47
233	24
233	47
232	24
232	47
231	24
231	47
230	24
230	47
229	24
229	47
228	24
228	47
227	24
227	47
226	24
226	47
225	24
225	47
224	24
224	47
223	24
223	47
222	24
222	47
221	24
221	47
220	24
220	47
219	24
219	47
218	23
218	46
217	23
217	46
216	23
216	46
215	23
215	45
214	23
214	45
213	23
213	45
212	23
212	45
211	23
211	45
210	23
210	45
209	23
209	45
208	23
208	45
207	23
207	45
206	23
206	45
205	23
205	45
204	23
204	45
203	23
203	45
202	23
202	45
201	23
201	45
200	23
200	45
199	23
199	45
198	23
198	45
197	23
197	45
196	23
196	45
195	23
195	45
194	23
194	45
193	23
193	45
192	23
192	45
191	23
191	45
190	23
190	45
189	23
189	45
188	22
188	43
187	22
187	43
186	22
186	43
185	22
185	43
184	22
184	43
183	22
183	43
182	22
182	43
181	22
181	43
180	22
180	43
179	22
179	43
178	22
178	43
177	22
177	43
176	22
176	43
175	22
175	43
174	22
174	43
173	22
173	43
172	22
172	43
171	22
171	43
170	22
170	43
169	22
169	43
168	22
168	43
167	22
167	43
166	22
166	43
165	22
165	43
164	22
164	43
163	22
163	43
162	22
162	43
161	21
161	42
160	21
160	41
159	21
159	41
158	21
158	41
157	21
157	41
156	21
156	41
155	21
155	41
154	21
154	41
153	21
153	41
152	21
152	41
151	21
151	41
150	21
150	41
149	21
149	41
148	21
148	41
147	21
147	41
146	21
146	41
145	21
145	41
144	21
144	41
143	21
143	41
142	21
142	41
141	21
141	41
140	20
140	40
139	20
139	39
138	20
138	39
137	20
137	39
136	20
136	39
135	20
135	39
134	20
134	39
133	20
133	39
132	20
132	39
131	20
131	39
130	20
130	39
129	20
129	39
128	20
128	39
127	20
127	39
126	20
126	39
125	19
125	38
124	19
124	37
123	19
123	37
122	19
122	37
121	19
121	37
120	19
120	37
119	19
119	37
118	19
118	37
117	19
117	37
116	19
116	37
115	19
115	37
114	19
114	37
113	19
113	37
112	19
112	37
111	19
111	37
110	18
110	35
109	18
109	35
108	18
108	35
107	18
107	35
106	18
106	35
105	18
105	35
104	18
104	35
103	18
103	35
102	18
102	35
101	18
101	35
100	17
100	33
99	17
99	33
98	17
98	33
97	17
97	33
96	17
96	33
95	17
95	33
94	17
94	33
93	17
93	33
92	17
92	33
91	17
91	33
90	17
90	33
89	17
89	33
88	17
88	33
87	16
87	31
86	16
86	31
85	16
85	31
84	16
84	31
83	16
83	31
82	16
82	31
81	16
81	31
80	16
80	31
79	16
79	31
78	16
78	31
77	15
77	29
76	15
76	29
75	15
75	29
74	15
74	29
73	15
73	29
72	15
72	29
71	15
71	29
70	15
70	29
69	15
69	29
68	15
68	29
67	14
67	27
66	14
66	27
65	14
65	27
64	14
64	27
63	14
63	27
62	14
62	27
61	14
61	27
60	14
60	27
59	13
59	26
58	13
58	25
57	13
57	25
56	13
56	25
55	13
55	25
54	13
54	25
53	13
53	25
52	13
52	25
51	13
51	25
50	13
50	25
49	12
49	23
48	12
48	23
47	12
47	23
46	11
46	22
45	11
45	22
44	11
44	21
43	11
43	21
42	11
42	21
41	10
41	19
40	10
40	19
39	10
39	19
38	10
38	19
37	10
37	19
36	9
36	18
35	9
35	18
34	9
34	18
33	9
33	18
32	9
32	17
31	9
31	17
30	9
30	17
29	8
29	16
28	8
28	16
27	8
27	15
26	8
26	15
25	8
25	15
24	7
24	14
23	7
23	13
22	6
22	12
21	6
21	11
20	6
20	11
19	5
19	10
18	5
18	10
17	5
17	9
16	5
16	9
15	4
15	8
14	4
14	7
13	3
13	6
12	3
12	5
11	3
11	5
10	3
10	5
9	3
9	5
8	2
8	4
7	2
7	4
6	2
6	3
5	2
5	3
4	1
4	2
3	1
3	1
2	1
2	1
1	1
1	1

392	28
392	55
391	28
391	55
390	28
390	55
389	28
389	55
388	28
388	55
387	28
387	55
386	28
386	55
385	28
385	55
384	28
384	55
383	28
383	55
382	28
382	55
381	28
381	55
380	28
380	55
379	28
379	55
378	28
378	55
377	28
377	55
376	28
376	55
375	28
375	55
374	28
374	55
373	28
373	55
372	28
372	55
371	28
371	55
370	28
370	55
369	28
369	55
368	28
368	55
367	28
367	55
366	28
366	55
365	28
365	55
364	28
364	55
363	28
363	55
362	28
362	55
361	28
361	55
360	28
360	55
359	28
359	55
358	28
358	55
357	28
357	55
356	28
356	55
355	28
355	55
354	28
354	55
353	28
353	55
352	27
352	53
351	27
351	53
350	27
350	53
349	27
349	53
348	27
348	53
347	27
347	53
346	27
346	53
345	27
345	53
344	27
344	53
343	27
343	53
342	27
342	53
341	27
341	53
340	27
340	53
339	27
339	53
338	27
338	53
337	27
337	53
336	27
336	53
335	27
335	53
334	27
334	53
333	27
333	53
332	27
332	53
331	27
331	53
330	27
330	53
329	27
329	53
328	27
328	53
327	27
327	53
326	27
326	53
325	27
325	53
324	27
324	53
323	27
323	53
322	27
322	53
321	27
321	53
320	27
320	53
319	27
319	53
318	27
318	53
317	27
317	53
316	26
316	51
315	26
315	51
314	26
314	51
313	26
313	51
312	26
312	51
311	26
311	51
310	26
310	51
309	26
309	51
308	26
308	51
307	26
307	51
306	26
306	51
305	26
305	51
304	26
304	51
303	26
303	51
302	26
302	51
301	26
301	51
300	26
300	51
299	26
299	51
298	26
298	51
297	26
297	51
296	26
296	51
295	26
295	51
294	26
294	51
293	26
293	51
292	26
292	51
291	26
291	51
290	26
290	51
289	26
289	51
288	26
288	51
287	26
287	51
286	26
286	51
285	26
285	51
284	26
284	51
283	26
283	51
282	26
282	51
281	25
281	50
280	25
280	50
279	25
279	49
278	25
278	49
277	25
277	49
276	25
276	49
275	25
275	49
274	25
274	49
273	25
273	49
272	25
272	49
271	25
271	49
270	25
270	49
269	25
269	49
268	25
268	49
267	25
267	49
266	25
266	49
265	25
265	49
264	25
264	49
263	25
263	49
262	25
262	49
261	25
261	49
260	25
260	49
259	25
259	49
258	25
258	49
257	25
257	49
256	25
256	49
255	25
255	49
254	25
254	49
253	25
253	49
252	25
252	49
251	25
251	49
250	25
250	49
249	25
249	49
248	25
248	49
247	25
247	49
246	25
246	49
245	25
245	49
244	24
244	48
243	24
243	47
242	24
242	47
241	24
241	47
240	24
240	47
239	24
239	47
238	24
238	47
237	24
237	47
236	24
236	47
235	24
235	47
234	24
234	47
233	24
233	47
232	24
232	47
231	24
231	47
230	24
230	47
229	24
229	47
228	24
228	47
227	24
227	47
226	24
226	47
225	24
225	47
224	24
224	47
223	24
223	47
222	24
222	47
221	24
221	47
220	24
220	47
219	24
219	47
218	23
218	46
217	23
217	46
216	23
216	46
215	23
215	45
214	23
214	45
213	23
213	45
212	23
212	45
211	23
211	45
210	23
210	45
209	23
209	45
208	23
208	45
207	23
207	45
206	23
206	45
205	23
205	45
204	23
204	45
203	23
203	45
202	23
202	45
201	23
201	45
200	23
200	45
199	23
199	45
198	23
198	45
197	23
197	45
196	23
196	45
195	23
195	45
194	23
194	45
193	23
193	45
192	23
192	45
191	23
191	45
190	23
190	45
189	23
189	45
188	22
188	43
187	22
187	43
186	22
186	43
185	22
185	43
184	22
184	43
183	22
183	43
182	22
182	43
181	22
181	43
180	22
180	43
179	22
179	43
178	22
178	43
177	22
177	43
176	22
176	43
175	22
175	43
174	22
174	43
173	22
173	43
172	22
172	43
171	22
171	43
170	22
170	43
169	22
169	43
168	22
168	43
167	22
167	43
166	22
166	43
165	22
165	43
164	22
164	43
163	22
163	43
162	22
162	43
161	21
161	42
160	21
160	41
159	21
159	41
158	21
158	41
157	21
157	41
156	21
156	41
155	21
155	41
154	21
154	41
153	21
153	41
152	21
152	41
151	21
151	41
150	21
150	41
149	21
149	41
148	21
148	41
147	21
147	41
146	21
146	41
145	21
145	41
144	21
144	41
143	21
143	41
142	21
142	41
141	21
141	41
140	20
140	40
139	20
139	39
138	20
138	39
137	20
137	39
136	20
136	39
135	20
135	39
134	20
134	39
133	20
133	39
132	20
132	39
131	20
131	39
130	20
130	39
129	20
129	39
128	20
128	39
127	20
127	39
126	20
126	39
125	19
125	38
124	19
124	37
123	19
123	37
122	19
122	37
121	19
121	37
120	19
120	37
119	19
119	37
118	19
118	37
117	19
117	37
116	19
116	37
115	19
115	37
114	19
114	37
113	19
113	37
112	19
112	37
111	19
111	37
110	18
110	35
109	18
109	35
108	18
108	35
107	18
107	35
106	18
106	35
105	18
105	35
104	18
104	35
103	18
103	35
102	18
102	35
101	18
101	35
100	17
100	33
99	17
99	33
98	17
98	33
97	17
97	33
96	17
96	33
95	17
95	33
94	17
94	33
93	17
93	33
92	17
92	33
91	17
91	33
90	17
90	33
89	17
89	33
88	17
88	33
87	16
87	31
86	16
86	31
85	16
85	31
84	16
84	31
83	16
83	31
82	16
82	31
81	16
81	31
80	16
80	31
79	16
79	31
78	16
78	31
77	15
77	29
76	15
76	29
75	15
75	29
74	15
74	29
73	15
73	29
72	15
72	29
71	15
71	29
70	15
70	29
69	15
69	29
68	15
68	29
67	14
67	27
66	14
66	27
65	14
65	27
64	14
64	27
63	14
63	27
62	14
62	27
61	14
61	27
60	14
60	27
59	13
59	26
58	13
58	25
57	13
57	25
56	13
56	25
55	13
55	25
54	13
54	25
53	13
53	25
52	13
52	25
51	13
51	25
50	13
50	25
49	12
49	23
48	12
48	23
47	12
47	23
46	11
46	22
45	11
45	22
44	11
44	21
43	11
43	21
42	11
42	21
41	10
41	19
40	10
40	19
39	10
39	19
38	10
38	19
37	10
37	19
36	9
36	18
35	9
35	18
34	9
34	18
33	9
33	18
32	9
32	17
31	9
31	17
30	9
30	17
29	8
29	16
28	8
28	16
27	8
27	15
26	8
26	15
25	8
25	15
24	7
24	14
23	7
23	13
22	6
22	12
21	6
21	11
20	6
20	11
19	5
19	10
18	5
18	10
17	5
17	9
16	5
16	9
15	4
15	8
14	4
14	7
13	3
13	6
12	3
12	5
11	3
11	5
10	3
10	5
9	3
9	5
8	2
8	4
7	2
7	4
6	2
6	3
5	2
5	3
4	1
4	2
3	1
3	1
2	1
2	1
1	1
1	1

392	28
392	55
391	28
391	55
390	28
390	55
389	28
389	55
388	28
388	55
387	28
387	55
386	28
386	55
385	28
385	55
384	28
384	55
383	28
383	55
382	28
382	55
381	28
381	55
380	28
380	55
379	28
379	55
378	28
378	55
377	28
377	55
376	28
376	55
375	28
375	55
374	28
374	55
373	28
373	55
372	28
372	55
371	28
371	55
370	28
370	55
369	28
369	55
368	28
368	55
367	28
367	55
366	28
366	55
365	28
365	55
364	28
364	55
363	28
363	55
362	28
362	55
361	28
361	55
360	28
360	55
359	28
359	55
358	28
358	55
357	28
357	55
356	28
356	55
355	28
355	55
354	28
354	55
353	28
353	55
352	27
352	53
351	27
351	53
350	27
350	53
349	27
349	53
348	27
348	53
347	27
347	53
346	27
346	53
345	27
345	53
344	27
344	53
343	27
343	53
342	27
342	53
341	27
341	53
340	27
340	53
339	27
339	53
338	27
338	53
337	27
337	53
336	27
336	53
335	27
335	53
334	27
334	53
333	27
333	53
332	27
332	53
331	27
331	53
330	27
330	53
329	27
329	53
328	27
328	53
327	27
327	53
326	27
326	53
325	27
325	53
324	27
324	53
323	27
323	53
322	27
322	53
321	27
321	53
320	27
320	53
319	27
319	53
318	27
318	53
317	27
317	53
316	26
316	51
315	26
315	51
314	26
314	51
313	26
313	51
312	26
312	51
311	26
311	51
310	26
310	51
309	26
309	51
308	26
308	51
307	26
307	51
306	26
306	51
305	26
305	51
304	26
304	51
303	26
303	51
302	26
302	51
301	26
301	51
300	26
300	51
299	26
299	51
298	26
298	51
297	26
297	51
296	26
296	51
295	26
295	51
294	26
294	51
293	26
293	51
292	26
292	51
291	26
291	51
290	26
290	51
289	26
289	51
288	26
288	51
287	26
287	51
286	26
286	51
285	26
285	51
284	26
284	51
283	26
283	51
282	26
282	51
281	25
281	50
280	25
280	50
279	25
279	49
278	25
278	49
277	25
277	49
276	25
276	49
275	25
275	49
274	25
274	49
273	25
273	49
272	25
272	49
271	25
271	49
270	25
270	49
269	25
269	49
268	25
268	49
267	25
267	49
266	25
266	49
265	25
265	49
264	25
264	49
263	25
263	49
262	25
262	49
261	25
261	49
260	25
260	49
259	25
259	49
258	25
258	49
257	25
257	49
256	25
256	49
255	25
255	49
254	25
254	49
253	25
253	49
252	25
252	49
251	25
251	49
250	25
250	49
249	25
249	49
248	25
248	49
247	25
247	49
246	25
246	49
245	25
245	49
244	24
244	48
243	24
243	47
242	24
242	47
241	24
241	47
240	24
240	47
239	24
239	47
238	24
238	47
237	24
237	47
236	24
236	47
235	24
235	47
234	24
234	47
233	24
233	47
232	24
232	47
231	24
231	47
230	24
230	47
229	24
229	47
228	24
228	47
227	24
227	47
226	24
226	47
225	24
225	47
224	24
224	47
223	24
223	47
222	24
222	47
221	24
221	47
220	24
220	47
219	24
219	47
218	23
218	46
217	23
217	46
216	23
216	46
215	23
215	45
214	23
214	45
213	23
213	45
212	23
212	45
211	23
211	45
210	23
210	45
209	23
209	45
208	23
208	45
207	23
207	45
206	23
206	45
205	23
205	45
204	23
204	45
203	23
203	45
202	23
202	45
201	23
201	45
200	23
200	45
199	23
199	45
198	23
198	45
197	23
197	45
196	23
196	45
195	23
195	45
194	23
194	45
193	23
193	45
192	23
192	45
191	23
191	45
190	23
190	45
189	23
189	45
188	22
188	43
187	22
187	43
186	22
186	43
185	22
185	43
184	22
184	43
183	22
183	43
182	22
182	43
181	22
181	43
180	22
180	43
179	22
179	43
178	22
178	43
177	22
177	43
176	22
176	43
175	22
175	43
174	22
174	43
173	22
173	43
172	22
172	43
171	22
171	43
170	22
170	43
169	22
169	43
168	22
168	43
167	22
167	43
166	22
166	43
165	22
165	43
164	22
164	43
163	22
163	43
162	22
162	43
161	21
161	42
160	21
160	41
159	21
159	41
158	21
158	41
157	21
157	41
156	21
156	41
155	21
155	41
154	21
154	41
153	21
153	41
152	21
152	41
151	21
151	41
150	21
150	41
149	21
149	41
148	21
148	41
147	21
147	41
146	21
146	41
145	21
145	41
144	21
144	41
143	21
143	41
142	21
142	41
141	21
141	41
140	20
140	40
139	20
139	39
138	20
138	39
137	20
137	39
136	20
136	39
135	20
135	39
134	20
134	39
133	20
133	39
132	20
132	39
131	20
131	39
130	20
130	39
129	20
129	39
128	20
128	39
127	20
127	39
126	20
126	39
125	19
125	38
124	19
124	37
123	19
123	37
122	19
122	37
121	19
121	37
120	19
120	37
119	19
119	37
118	19
118	37
117	19
117	37
116	19
116	37
115	19
115	37
114	19
114	37
113	19
113	37
112	19
112	37
111	19
111	37
110	18
110	35
109	18
109	35
108	18
108	35
107	18
107	35
106	18
106	35
105	18
105	35
104	18
104	35
103	18
103	35
102	18
102	35
101	18
101	35
100	17
100	33
99	17
99	33
98	17
98	33
97	17
97	33
96	17
96	33
95	17
95	33
94	17
94	33
93	17
93	33
92	17
92	33
91	17
91	33
90	17
90	33
89	17
89	33
88	17
88	33
87	16
87	31
86	16
86	31
85	16
85	31
84	16
84	31
83	16
83	31
82	16
82	31
81	16
81	31
80	16
80	31
79	16
79	31
78	16
78	31
77	15
77	29
76	15
76	29
75	15
75	29
74	15
74	29
73	15
73	29
72	15
72	29
71	15
71	29
70	15
70	29
69	15
69	29
68	15
68	29
67	14
67	27
66	14
66	27
65	14
65	27
64	14
64	27
63	14
63	27
62	14
62	27
61	14
61	27
60	14
60	27
59	13
59	26
58	13
58	25
57	13
57	25
56	13
56	25
55	13
55	25
54	13
54	25
53	13
53	25
52	13
52	25
51	13
51	25
50	13
50	25
49	12
49	23
48	12
48	23
47	12
47	23
46	11
46	22
45	11
45	22
44	11
44	21
43	11
43	21
42	11
42	21
41	10
41	19
40	10
40	19
39	10
39	19
38	10
38	19
37	10
37	19
36	9
36	18
35	9
35	18
34	9
34	18
33	9
33	18
32	9
32	17
31	9
31	17
30	9
30	17
29	8
29	16
28	8
28	16
27	8
27	15
26	8
26	15
25	8
25	15
24	7
24	14
23	7
23	13
22	6
22	12
21	6
21	11
20	6
20	11
19	5
19	10
18	5
18	10
17	5
17	9
16	5
16	9
15	4
15	8
14	4
14	7
13	3
13	6
12	3
12	5
11	3
11	5
10	3
10	5
9	3
9	5
8	2
8	4
7	2
7	4
6	2
6	3
5	2
5	3
4	1
4	2
3	1
3	1
2	1
2	1
1	1
1	1