A002338 x such that p = (x^2 + 27*y^2)/4, where p is the n-th prime of the form 3k+1. (Formerly M3754 N1531)

1, 5, 7, 4, 11, 8, 1, 5, 7, 17, 19, 13, 2, 20, 23, 19, 14, 25, 7, 23, 11, 13, 28, 22, 17, 29, 26, 32, 16, 35, 1, 5, 37, 35, 13, 29, 34, 31, 19, 2, 28, 10, 23, 25, 32, 43, 29, 1, 31, 11, 26, 49, 47, 17, 43, 40, 49, 37, 8, 53, 44, 50, 16, 41, 29, 49, 31, 56, 5, 7, 35, 13, 59, 47, 19, 52, 61, 41, 61, 10, 43, 14, 53, 59, 64, 65, 62, 55, 22, 65, 35, 67, 7

Offset

1,2

Comments

A123489 is a signed version. - Michael Somos, Aug 27 2012

References

A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.

B. Engquist and Wilfried Schmid, Mathematics Unlimited - 2001 and Beyond, Chapter on Error-correcting codes and curves over finite fields, see pp. 1118-1119. [From Neven Juric, Oct 16 2008.]

D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.

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

Ruperto Corso, Table of n, a(n) for n = 1..1000

A. J. C. Cunningham, Quadratic Partitions, Hodgson, London, 1904 [Annotated scans of selected pages]

S. R. Finch, Powers of Euler's q-Series, (arXiv:math.NT/0701251).

Mathematica

Reap[For[p = 2, p<2000, p = NextPrime[p], For[x = 1, x <= Floor[2Sqrt[p]], x++, px = 4p - x^2; If[Mod[px, 27] == 0, If[IntegerQ[Sqrt[px/27]], Sow[x] ]]]]][[2, 1]] (* Jean-François Alcover, Sep 06 2018, after Ruperto Corso *)

Prog

(PARI) forprime(p=2, 10000, for(x=1, floor(2*sqrt(p)), px=4*p-x^2; if(px%27==0, if(issquare(px/27, &y), print1(x", "))))) /* Ruperto Corso, Dec 14 2011 */

Crossrefs

Cf. A002339, A123489.

Sequence in context: A096437 A096458 A123489 * A324791 A226021 A242059

Adjacent sequences: A002335 A002336 A002337 * A002339 A002340 A002341

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Corrected and extended by Ruperto Corso, Dec 14 2011

Status

approved