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 A002339 y such that p = (x^2 + 27y^2 )/4. (Formerly M0058 N0043) 2

%I M0058 N0043

%S 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,

%T 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,

%U 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

%N y such that p = (x^2 + 27y^2 )/4.

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

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

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Ruperto Corso, <a href="/A002339/b002339.txt">Table of n, a(n) for n = 1..1000</a>

%H A. J. C. Cunningham, <a href="/A002330/a002330.pdf">Quadratic Partitions</a>, Hodgson, London, 1904 [Annotated scans of selected pages]

%H S. R. Finch, <a href="http://arXiv.org/abs/math.NT/0701251">Powers of Euler's q-Series</a>, (arXiv:math.NT/0701251).

%o (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(y","))))) /* _Ruperto Corso_, Dec 14 2011 */

%Y Cf. A002338.

%K nonn

%O 1,4

%A _N. J. A. Sloane_

%E Corrected and extended by _Ruperto Corso_, Dec 14 2011

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