The OEIS is supported by the many generous donors to the OEIS Foundation.
%I M0109 N0042 #18 Oct 15 2023 01:41:37
%S 1,1,1,1,2,1,2,3,1,3,1,4,1,1,2,4,5,5,1,2,3,6,3,1,5,2,4,1,7,5,3,5,7,1,
%T 5,7,3,1,4,5,6,8,1,2,7,9,4,5,3,5,2,1,9,5,6,7,10,11,3,1,4,11,6,7,8,9,7,
%U 1,4,9,5,3,8,13,3,1,4,11,1,8,2,9,10,11,13,14,7,4,5,11,7,2,10,11,15,5,9
%N Least positive integer y such that p = (x^2 - 5*y^2)/4 where p is the n-th odd prime such that 5 is a square mod p.
%C The n-th odd prime for which 5 is a square mod p is A038872(n).
%D A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.
%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 A. J. C. Cunningham, <a href="/A002330/a002330.pdf">Quadratic Partitions</a>, Hodgson, London, 1904. [Annotated scans of selected pages]
%e 5 = (5^2 - 5*1^2)/4 so a(1)=1;
%e 11 = (7^2 - 5*1^2)/4 so a(2)=1.
%o (PARI) a(n)=local(y,p); if(n<1,0,p=0; y=1; until(p>=n,y++; if(issquare(5+O(prime(y))),p++)); p=prime(y); y=0; until(issquare(4*p+5*y^2),y++); y)
%Y Cf. A002342.
%Y Cf. A002342, A038872.
%K nonn
%O 1,5
%A _N. J. A. Sloane_