%I A002331 M0096 N0033
%S A002331 1,1,2,1,2,1,4,2,5,3,5,4,1,3,7,4,7,6,2,9,7,1,2,8,4,1,10,9,5,2,12,11,
%T A002331 9,5,8,7,10,6,1,3,14,12,7,4,10,5,11,10,14,13,1,8,5,17,16,4,13,6,12,
%U A002331 1,5,15,2,9,19,12,17,11,5,14,10,18,4,6,16,20,19,10,13,4,6,15,22,11,3,5
%N A002331 Values of x in the solution to p = x^2 + y^2, x <= y, with prime p = 
               A002313(n).
%D A002331 A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 
               1.
%D A002331 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002331 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002331 J. Todd, A problem on arc tangent relations, Amer. Math. Monthly, 56 
               (1949), 517-528.
%H A002331 T. D. Noe, <a href="b002331.txt">Table of n, a(n) for n=1..1000</a>
%H A002331 K. Matthews, <a href="http://www.numbertheory.org/php/serret.html">Serret's 
               algorithm Server</a>
%H A002331 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Fermats4nPlus1Theorem.html">Fermat's 4n Plus 1 Theorem</a>
%F A002331 Equals A096029(n)-A096030(n) for entries after the first. - Lekraj Beedassy 
               (blekraj(AT)yahoo.com), Jul 16 2004
%e A002331 The following table shows the relationship
%e A002331 between several closely related sequences:
%e A002331 Here p = A002144 = primes == 1 mod 4, p = a^2+b^2 with a < b;
%e A002331 a = A002331, b = A002330, t_1 = ab/2 = A070151;
%e A002331 p^2 = c^2+d^2 with c < d; c = A002366, d = A002365,
%e A002331 t_2 = 2ab = A145046, t_3 = b^2-a^2 = A070079,
%e A002331 with {c,d} = {t_2, t_3}, t_4 = cd/2 = ab(b^2-a^2).
%e A002331 ---------------------------------
%e A002331 .p..a..b..t_1..c...d.t_2.t_3..t_4
%e A002331 ---------------------------------
%e A002331 .5..1..2...1...3...4...4...3....6
%e A002331 13..2..3...3...5..12..12...5...30
%e A002331 17..1..4...2...8..15...8..15...60
%e A002331 29..2..5...5..20..21..20..21..210
%e A002331 37..1..6...3..12..35..12..35..210
%e A002331 41..4..5..10...9..40..40...9..180
%e A002331 53..2..7...7..28..45..28..45..630
%e A002331 .................................
%p A002331 See A002330 for Maple program.
%Y A002331 Cf. A002330, A002313, A002144.
%Y A002331 Sequence in context: A029196 A051493 A029173 this_sequence A060805 A030767 
               A135545
%Y A002331 Adjacent sequences: A002328 A002329 A002330 this_sequence A002332 A002333 
               A002334
%K A002331 nonn
%O A002331 1,3
%A A002331 N. J. A. Sloane (njas(AT)research.att.com).