cp's OEIS Frontend

A002342 Least positive integer x 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.

%I A002342 M3758 N1534 #17 Oct 15 2023 01:41:41
%S A002342 5,7,9,11,12,13,16,17,17,19,19,22,21,23,24,26,27,29,27,28,29,32,31,31,
%T A002342 33,32,34,33,37,37,37,39,41,39,41,43,41,41,42,43,44,46,43,44,47,49,46,
%U A002342 47,47,49,48,49,53,51,52,53,56,57,53,53,54,59,56,57,58,59,59,57,58,61
%N A002342 Least positive integer x 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 A002342 The n-th odd prime for which 5 is a square mod p is A038872(n).
%D A002342 A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.
%D A002342 D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.
%D A002342 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002342 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002342 A. J. C. Cunningham, <a href="/A002330/a002330.pdf">Quadratic Partitions</a>, Hodgson, London, 1904. [Annotated scans of selected pages]
%e A002342 5 = (5^2 - 5*1^2)/4 so a(1)=5;
%e A002342 11 = (7^2 - 5*1^2)/4 so a(2)=7.
%o A002342 (PARI) a(n)=local(y,p); if(n<1,0,p=0; y=2; until(p>=n,y++; if(issquare(5+O(prime(y))),p++)); p=prime(y); y=0; until(issquare(4*p+5*y^2),y++); sqrtint(4*p+5*y^2))
%Y A002342 Cf. A002343, A038872.
%K A002342 nonn
%O A002342 1,1
%A A002342 _N. J. A. Sloane_