This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A262025 #7 Sep 20 2015 06:50:00 %S A262025 1,4,2,9,3,324,7,16,8,4,27,98,25,63,4900,5,11,17,36,18,12,1024,6,99, %T A262025 80,12167,49,324,33124,242,44,7,75,9801,15,883159524,31,64,32,16,3887, %U A262025 125,8,1140624,1849,28899,175,26,81,27,142884,5202,250000,9,575,6075,1071647,19,31404816,49,100,50,20,16040025,675,79035335993124,10,147,63,602176,512,4900,324,153458 %N A262025 a(n) = (A262024(n)-1)/2: a(n)*(a(n) + 1) = d(n)*Y(n)^2 with d(n) = A007969 and Y(n) = A261250(n). %C A262025 The positive fundamental solutions (x0(n), y0(n)) of the Pell equation x^2 - d(n) y^2 = +1, with d not a square, have only even y solutions for d(n) = A007969 (Conway's products of 1-happy couples). The proof is now given in the W. Lang link under A007969. The solutions x0 and y0 = 2*Y0 are given in A262024 and 2*A261250, respectively. The numbers X0(n) = (x0(n) - 1)/2 = a(n) satisfy a(n)*(a(n) + 1) = d(n)*Y0(n)^2. See the mentioned link. %Y A262025 Cf. A007969, A007970, A262024, A261250. %K A262025 nonn %O A262025 1,2 %A A262025 _Wolfdieter Lang_, Sep 19 2015