

A002338


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


2



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
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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 Errorcorrecting codes and curves over finite fields, see pp. 11181119. [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 qSeries, (arXiv:math.NT/0701251).


PROG

(PARI) forprime(p=2, 10000, for(x=1, floor(2*sqrt(p)), px=4*px^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 * A226021 A242059 A178668
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



