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

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A002639 A002640 A002641 * A002643 A002644 A002645

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved