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%I M4606 N1131 #25 Oct 17 2023 08:19:14
%S 9,29,35,42,48,113,120,126,152,185,204,224,237,243,276,302,308,321,
%T 341,386,399,419,432,477,503,510,516,542,549,588,633,659,666,705,731,
%U 770,776,783,789,815,848,854,887,906,932,945,965,978
%N Numbers k such that (k^2 + k + 1)/13 is prime.
%C All terms are congruent to 3 or 9 (mod 13). [_Bruno Berselli_, Sep 26 2012]
%D A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 1, pp. 245-259.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A002642/b002642.txt">Table of n, a(n) for n = 1..1000</a>
%H A. J. C. Cunningham, <a href="/A001912/a001912.pdf">Binomial Factorisations</a>, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]
%t Select[Range[1000], PrimeQ[(#^2 + # + 1)/13]&] (* _Vincenzo Librandi_, Sep 25 2012 *)
%o (PARI) forstep(n=9,1e4,[7,6],if(isprime((n^2+n+1)/13),print1(n", "))) \\ _Charles R Greathouse IV_, Sep 25 2012
%o (Magma)
%o I:=[m: m in [1..1000] | m mod 13 in [3,9]];
%o [n: n in I | IsPrime( (n^2 + n + 1) div 13 )];
%o // _Bruno Berselli_, Sep 26 2012
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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