A276262 Centered 22-gonal primes.

23, 67, 331, 463, 617, 991, 1453, 2003, 2311, 4621, 6073, 7151, 7723, 8317, 8933, 11617, 12343, 14653, 15467, 18041, 19867, 25873, 26951, 28051, 29173, 37643, 41603, 42967, 51613, 61051, 62701, 64373, 66067, 67783, 73063, 78541, 94117, 102433, 117833, 120121, 131891, 136753

Offset: 1

Author

Ilya Gutkovskiy, Aug 26 2016

Keywords

• nonn

Comments

Primes of the form 11*k^2 + 11*k + 1.

Numbers k such that 11*k^2 + 11*k + 1 is prime: 1, 2, 5, 6, 7, 9, 11, 13, 14, 20, 23, 25, 26, 27, 28, 32, 33, 36, 37, 40, 42, 48, 49, 50, 51, ...

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• OEIS Wiki, Centered polygonal numbers
• Eric Weisstein's World of Mathematics, Centered Polygonal Number
• Index entries for sequences related to centered polygonal numbers

Crossrefs

Cf. A000040, A069173.

Cf. centered k-gonal primes listed in A276261.

Programs

Magma

[k: n in [1..120] | IsPrime(k) where k is 11*n^2-11*n+1]; // Vincenzo Librandi, Aug 29 2016

Maple

select(isprime, [seq(11*k^2+11*k+1, k=1..1000)]);

Mathematica

Intersection[Table[11 k^2 + 11 k + 1, {k, 0, 1000}], Prime[Range[13000]]]
Select[Table[11n^2+11n+1,{n,150}],PrimeQ] (* Harvey P. Dale, Nov 22 2023 *)

PARI

lista(nn) = for(n=1, nn, if(isprime(p=11*n^2 + 11*n + 1), print1(p, ", "))); \\ Altug Alkan, Aug 26 2016