A002640 Numbers k such that (k^2 + k + 1)/3 is prime. (Formerly M3301 N1331)

4, 7, 10, 13, 19, 28, 31, 34, 40, 43, 52, 70, 73, 76, 82, 85, 91, 97, 103, 112, 115, 124, 127, 136, 145, 148, 157, 166, 175, 187, 190, 199, 202, 223, 241, 244, 259, 265, 271, 274, 280, 286, 316, 325, 358, 370, 376, 385, 388, 409, 421, 427, 442, 460, 469, 472

Offset

1,1

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[500], PrimeQ[(#^2 + # + 1)/3] &] (* Vincenzo Librandi, Sep 25 2012 *)

Prog

(Magma) [n: n in [4..500] | IsPrime((n^2+n+1) div 3)]; // Vincenzo Librandi, Nov 18 2010
(PARI) is(n)=isprime((n^2+n+1)/3) \\ Charles R Greathouse IV, Jun 06 2017

Crossrefs

Sequence in context: A348156 A287555 A008470 * A096675 A069212 A091290

Adjacent sequences: A002637 A002638 A002639 * A002641 A002642 A002643

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved