

A002339


y such that p = (x^2 + 27y^2 )/4.
(Formerly M0058 N0043)


2



1, 1, 1, 2, 1, 2, 3, 3, 3, 1, 1, 3, 4, 2, 1, 3, 4, 1, 5, 3, 5, 5, 2, 4, 5, 3, 4, 2, 6, 1, 7, 7, 1, 3, 7, 5, 4, 5, 7, 8, 6, 8, 7, 7, 6, 3, 7, 9, 7, 9, 8, 1, 3, 9, 5, 6, 3, 7, 10, 1, 6, 4, 10, 7, 9, 5, 9, 2, 11, 11, 9, 11, 1, 7, 11, 6, 1, 9, 3, 12, 9, 12, 7, 5, 2, 1, 4, 7, 12, 3, 11, 1, 13, 13, 7, 13, 13, 11, 9, 11, 5, 13, 9, 3, 14, 13, 6, 14, 5, 13, 7, 10, 2, 13, 1, 15, 3, 15
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OFFSET

1,4


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(y", "))))) /* Ruperto Corso, Dec 14 2011 */


CROSSREFS

Cf. A002338.
Sequence in context: A123265 A104345 A244516 * A123243 A037193 A003986
Adjacent sequences: A002336 A002337 A002338 * A002340 A002341 A002342


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Corrected and extended by Ruperto Corso, Dec 14 2011


STATUS

approved



