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A002642
Numbers k such that (k^2 + k + 1)/13 is prime.
(Formerly M4606 N1131)
3
9, 29, 35, 42, 48, 113, 120, 126, 152, 185, 204, 224, 237, 243, 276, 302, 308, 321, 341, 386, 399, 419, 432, 477, 503, 510, 516, 542, 549, 588, 633, 659, 666, 705, 731, 770, 776, 783, 789, 815, 848, 854, 887, 906, 932, 945, 965, 978
OFFSET
1,1
COMMENTS
All terms are congruent to 3 or 9 (mod 13). [Bruno Berselli, Sep 26 2012]
REFERENCES
A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 1, pp. 245-259.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]
MATHEMATICA
Select[Range[1000], PrimeQ[(#^2 + # + 1)/13]&] (* Vincenzo Librandi, Sep 25 2012 *)
PROG
(PARI) forstep(n=9, 1e4, [7, 6], if(isprime((n^2+n+1)/13), print1(n", "))) \\ Charles R Greathouse IV, Sep 25 2012
(Magma)
I:=[m: m in [1..1000] | m mod 13 in [3, 9]];
[n: n in I | IsPrime( (n^2 + n + 1) div 13 )];
// Bruno Berselli, Sep 26 2012
CROSSREFS
Sequence in context: A205144 A258483 A044976 * A032700 A322946 A350963
KEYWORD
nonn,easy
STATUS
approved