A069125 -id:A069125 - cp's OEIS frontend

A244911 Table read by antidiagonals: T(n,k) = n*k + T(n-1,k) for n >=1, T(0,k) = 1.

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 7, 7, 1, 1, 5, 10, 13, 11, 1, 1, 6, 13, 19, 21, 16, 1, 1, 7, 16, 25, 31, 31, 22, 1, 1, 8, 19, 31, 41, 46, 43, 29, 1, 1, 9, 22, 37, 51, 61, 64, 57, 37, 1, 1, 10, 25, 43, 61, 76, 85, 85, 73, 46, 1, 1, 11, 28, 49, 71, 91, 106, 113, 109, 91

Offset: 0

Kival Ngaokrajang, Jul 07 2014

T(n,k) is the total number of boxes, when we start with 1 center box (n = 0) then expand 1 box on k-arms for each n iteration. See illustration in links.
It seems that column C(k) = centered k-gonal numbers, and row R(n) = A000217(n)*k + 1.
The triangle under the main diagonal is A121722.
Column N (CN) is the Narayana transform (A001263) of (1, N, 0, 0, 0, ...). Example: C2 (1, 3, 7, 13, ...) is the Narayana transform of (1, 2, 0, 0, 0, ...). - Gary W. Adamson, Oct 01 2015

			Table begins:
       C0  C1  C2  C3  C4  C5
  n/k  0   1   2   3   4   5   ...
R0 0   1   1   1   1   1   1   ...
R1 1   1   2   3   4   5   6   ...
R2 2   1   4   7   10  13  16  ...
R3 3   1   7   13  19  25  31  ...
R4 4   1   11  21  31  41  51  ...
R5 5   1   16  31  46  61  76  ...
R6 6   1   22  43  64  85  106 ...
R7 7   1   29  57  85  113 141 ...
R8 8   1   37  73  109 145 181 ...
R9 9   1   46  91  136 181 226 ...
  ...  ... ... ... ... ... ... ...
C1 = A000124, C2 = A002061, C3 = A005448, C4 = A001844, C5 = A005891, C6 = A003215, C7 = A069099, C8 = A016754, C9 = A060544, C10 = A062786, C11 = A069125, C12  =  A003154.
R1 = A000027, R2 = A016777, R3 = A016921, R4 = A017281, R5 = 15*k + 1, R6 = A215146, R7 = A161714.

Kival Ngaokrajang, Illustration for n = 0..3, k = 1..4

Cf. A000217, A121722, A000124, A002061, A005448, A001844, A005891, A003215, A069099, A016754, A060544, A062786, A069125, A003154, A000027, A016777, A016921, A017281, A215146, A161714.

T(n,k) = n*k + T(n-1,k) for n >=1, T(0,k) = 1.

A262344 Centered 11-gonal (or hendecagonal) primes.

Original entry on oeis.org

67, 397, 727, 859, 1321, 2311, 3037, 3301, 4159, 8581, 10891, 12409, 19471, 28909, 47059, 51217, 63559, 64747, 78541, 79861, 95107, 100981, 108571, 119659, 134707, 139921, 156157, 177211, 195427, 203809, 221101, 257797, 264991, 284659, 287167, 294757, 307627, 315481

Offset: 1

Ilya Gutkovskiy, Nov 26 2015

nonn

Primes of the form (11*k^2 - 11*k + 2)/2.

OEIS Wiki, Figurate numbers
Eric Weisstein's World of Mathematics, Centered Polygonal Number
Eric Weisstein's World of Mathematics, Prime Number

Intersection of A069125 and A000040.

select(isprime, [(11*k^2-11*k+2)/2$k=1..300])[];  # Alois P. Heinz, May 27 2022

for(n=1, 1e3, if(isprime(k=(11*n^2-11*n+2)/2), print1(k,", "))) \\ Altug Alkan, Nov 26 2015

a(15)=47059 inserted by Georg Fischer, May 27 2022

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A244911 Table read by antidiagonals: T(n,k) = n*k + T(n-1,k) for n >=1, T(0,k) = 1.

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A262344 Centered 11-gonal (or hendecagonal) primes.

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