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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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]

Programs

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

Mathematica

Select[Range[1000], PrimeQ[(#^2 + # + 1)/13]&] (* Vincenzo Librandi, Sep 25 2012 *)

PARI

forstep(n=9,1e4,[7,6],if(isprime((n^2+n+1)/13),print1(n", "))) \\ Charles R Greathouse IV, Sep 25 2012