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%I #18 Nov 22 2023 11:54:50
%S 23,67,331,463,617,991,1453,2003,2311,4621,6073,7151,7723,8317,8933,
%T 11617,12343,14653,15467,18041,19867,25873,26951,28051,29173,37643,
%U 41603,42967,51613,61051,62701,64373,66067,67783,73063,78541,94117,102433,117833,120121,131891,136753
%N Centered 22-gonal primes.
%C Primes of the form 11*k^2 + 11*k + 1.
%C 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, ...
%H Robert Israel, <a href="/A276262/b276262.txt">Table of n, a(n) for n = 1..10000</a>
%H OEIS Wiki, <a href="http://oeis.org/wiki/Centered_polygonal_numbers#cite_note-1">Centered polygonal numbers</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CenteredPolygonalNumber.html">Centered Polygonal Number</a>
%H <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>
%p select(isprime, [seq(11*k^2+11*k+1, k=1..1000)]);
%t Intersection[Table[11 k^2 + 11 k + 1, {k, 0, 1000}], Prime[Range[13000]]]
%t Select[Table[11n^2+11n+1,{n,150}],PrimeQ] (* _Harvey P. Dale_, Nov 22 2023 *)
%o (PARI) lista(nn) = for(n=1, nn, if(isprime(p=11*n^2 + 11*n + 1), print1(p, ", "))); \\ _Altug Alkan_, Aug 26 2016
%o (Magma) [k: n in [1..120] | IsPrime(k) where k is 11*n^2-11*n+1]; // _Vincenzo Librandi_, Aug 29 2016
%Y Cf. A000040, A069173.
%Y Cf. centered k-gonal primes listed in A276261.
%K nonn
%O 1,1
%A _Ilya Gutkovskiy_, Aug 26 2016