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👁 Image Palindromic Nonagonals (or 9-gonals) (or enneagonal)
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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 : , ,

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

PLAIN TEXT POLYGONS

Normal and Palindromic Nonagonals

This basenumber
has digits
yielding the following palindromic nonagonal number

with a length of digits.

👁 bu17
A palindromic nonagonal numbers can only end with digit , , , , , and .
Alas, my palindromes may not have leading 's! So the zero option must not be investigated.

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

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

can only be followed by 2 or 7 : 52 or 57

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

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

👁 bu17
There exist no palindromic nonagonals of length

('s A082722)

Case Nona	Change of variables	CUDApalin parameters	Base Correction
odd base	n = 2 * m + 1		CUDAbase * 2 + 1
even base	n = 2 * m + 2		CUDAbase * 2 + 2

👁 bu17
's A048909 gives the first numbers that are both .

, , , , , , ...

Consult also 's page Nonagonal Triangular Number.

👁 bu17
's A036411 gives the first numbers that are both .

, , , , , ...

Consult also 's page Nonagonal Square Number.

👁 bu17
's A048915 gives the first numbers that are both .

, , , , , ...

Consult also 's page Nonagonal Pentagonal Number.

👁 bu17
's A048918 gives the first numbers that are both .

, , , , , ...

Consult also 's page Nonagonal Hexagonal Number.

👁 bu17
's A048921 gives the first numbers that are both .

, , , , ...

Consult also 's page Nonagonal Heptagonal Number.

👁 bu17
's A048924 gives the first numbers that are both .

, , , , ...

Consult also 's page Nonagonal Octagonal Number.

👁 bu17
The best way to get a 'structural' insight as how to imagine nonagonals is to visit for instance this site :

From 's Math Encyclopedia : Nonagonal Number

Sources Revealed

's Encyclopedia can be consulted online :

Neil Sloane's Integer Sequences

One can find the regular nonagonal numbers at

%N under A001106.

The palindromic nonagonal numbers are categorised as follows :

%N under A055560.

%N under A082723.

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

The Table

Index Nr			Length
Index Nr			Length
68	Info	28
68	56
67	Info	28
67	56
66	Info	28
66	56
65	Info	28
65	55
64	Info	28
64	55
63	Info	28
63	55
62	Info	27
62	54
61	Info	27
61	54
60	Info	25
60	50
59	Info	24
59	47
58	Info	23
58	45
57	Info	22
57	43
56	Info	22
56	43
55	Info	21
55	42
54	Info	21
54	42
53	Info	20
53	40
52	Info	20
52	40
51	Info	20
51	39
50	Info	20
50	39
49	Info	19
49	38
48	Info	19
48	38
47	Info	19
47	37
46	Info	18
46	37
45	Info	18
45	36
44	Info	17
44	34
43	Info	17
43	33
42	Info	17
42	33
41	Info	17
41	33
40	Info	17
40	33
39	Info	13
39	26
38	Info	13
38	26
37	Info	13
37	26
36	Info	12
36	24
35	Info	12
35	24
34	Info	12
34	23
33	Info	12
33	23
32	Info	11
32	23
31	Info	11
31	22
30	Info	11
30	21
29	Info	10
29	19
28	Info	10
28	19
27	Info	9
27	19
26	Info	9
26	18
25	Info	9
25	18
24	Info	9
24	17
23	Info	6
23	12
22	Info	6
22	12
21	Info	6
21	11
20	Info	5
20	10
19	Info	5
19	10
18	Info	5
18	9
17	Info	5
17	9
16	Info	5
16	9
15	Info	5
15	9
14	Info	5
14	9
13	Info	4
13	8
12	Info	4
12	8
11	Info	4
11	7
10	Info	4
10	7
9	Info	3
9	5
8	Info	2
8	5
7	Info	2
7	4
6	Info	2
6	3
5	Info	2
5	3
4	Info	1
4	3
3	Info	1
3	1
2	Info	1
2	1
1	Info	1
1	1

Contributions

(email) from Washington State, USA, discovered the palindromic nonagonals
starting from index number [] up to [].

[ ]
(email) from Washington State, USA, discovered the palindromic nonagonals
starting from index number [] up to [].

Higher values up to were found and submitted by .

Exhaustive (re)-search performed up to by and found no missers.

[ ]
(email) added four missing entries [], [], [] and [].

[ ]
(email) added two missing entries [] and [].

[ ]
(email) using Rust code by (email) discovered a record entry [].

[ ]
(email) added one missing entry [].

[ ]
(email) using CUDA code by (email) did a search for 53-digit palindromic nonagonals but there are none.
So he pushed through to 54 digits and found two new record entries [] and [], one with even root and one with odd root.

[ ]
(email) using CUDApalin from added three more entries [] up to [].

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- Last modified : September 27, 2024.

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E-mail address : pdg@worldofnumbers.com

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

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