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A300302
Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the k-th positive number whose binary representation contains the binary representation of n as a substring.
1
1, 2, 2, 3, 4, 3, 4, 6, 5, 4, 5, 8, 7, 6, 5, 6, 10, 9, 11, 8, 6, 7, 12, 11, 12, 12, 9, 7, 8, 14, 13, 13, 16, 13, 10, 8, 9, 16, 15, 14, 20, 17, 14, 11, 9, 10, 18, 17, 23, 22, 21, 18, 15, 12, 10, 11, 20, 19, 24, 28, 24, 22, 19, 19, 13, 11, 12, 22, 21, 25, 32, 29
OFFSET
1,2
COMMENTS
Each positive number k appears A122953(k) times in this array.
FORMULA
T(n, 1) = n.
T(n, 2) = 2*n.
T(n, 3) = 2*n + 1.
T(1, n) = A000027(n).
T(2, n) = A062289(n).
T(3, n) = A004780(n).
T(4, n) = A004753(n).
T(5, n) = A004748(n).
T(6, n) = A004749(n).
T(7, n) = A004781(n).
T(8, n) = A004779(n-1).
T(10, n) = A132782(n).
EXAMPLE
Square array begins:
n\k| 1 2 3 4 5 6 7 8 9 10
---+--------------------------------------------------
1| 1 2 3 4 5 6 7 8 9 10 <-- A000027
2| 2 4 5 6 8 9 10 11 12 13 <-- A062289
3| 3 6 7 11 12 13 14 15 19 22 <-- A004780
4| 4 8 9 12 16 17 18 19 20 24 <-- A004753
5| 5 10 11 13 20 21 22 23 26 27 <-- A004748
6| 6 12 13 14 22 24 25 26 27 28 <-- A004749
7| 7 14 15 23 28 29 30 31 39 46 <-- A004781
8| 8 16 17 24 32 33 34 35 40 48 <-- A004779
9| 9 18 19 25 36 37 38 39 41 50
10| 10 20 21 26 40 41 42 43 52 53 <-- A132782
PROG
(Perl) See Links section.
KEYWORD
nonn,base,tabl
AUTHOR
Rémy Sigrist, Mar 08 2018
STATUS
approved