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 A002642 Numbers n such that (n^2 + n + 1)/13 is prime. (Formerly M4606 N1131) 2

%I M4606 N1131

%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 n such that (n^2 + n + 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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Last modified July 20 16:15 EDT 2019. Contains 325185 sequences. (Running on oeis4.)