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A173330 First of two intermediate sequences for integral solution of A002144(n)=x^2+y^2.

%I A173330 #2 Mar 30 2012 18:51:05
%S A173330 1,10,1,5,1,5,46,5,70,5,9,1,106,106,126,142,146,13,9,186,1,214,13,226,
%T A173330 1,13,9,5,17,13,306,9,5,17,366,17,378,1,406,406,17,442,21,442,5,510,
%U A173330 21,538,13,1,570,5,17,598,25,13,25,650,1,5,694,706,9,742,25,17,786,5,25
%N A173330 First of two intermediate sequences for integral solution of A002144(n)=x^2+y^2.
%C A173330 A002972(n) = MIN(a(n), A002144(n) - a(n)).
%D A173330 H. Davenport, The Higher Arithmetic (Cambridge University Press 7th ed., 1999), ch. V.3, p.122.
%F A173330 a(n) = (2k)! / 2(k!)^2 mod p, where p = 4*k+1 = A002144(n).
%e A173330 n=7: A002144(7) = 53 = 4*13 + 1,
%e A173330 a(7) = 26! / (2*(13!)^2) mod 53 = 403291461126605635584000000/77551576087265280000 mod 53 = 5200300 mod 53 = 46,
%e A173330 A002972(7) = MIN(46, 53 - 46) = 7;
%e A173330 n=8: A002144(8) = 61 = 4*15 + 1,
%e A173330 a(8) = 30! / (2*(15!)^2) mod 61 = 265252859812191058636308480000000/3420024505448398848000000 mod 61 = 77558760 mod 61 = 5,
%e A173330 A002972(8) = MIN(5, 61 - 5) = 5.
%Y A173330 Cf. A173331, A001700, A010050, A000142, A005098.
%K A173330 nonn
%O A173330 1,2
%A A173330 _Reinhard Zumkeller_, Feb 16 2010