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 A254763 #11 Feb 14 2015 23:40:38 %S A254763 2,4,6,5,4,8,7,9,7,6,11,14,9,7,16,11,15,18,8,14,20,10,9,19,15,22,14, %T A254763 13,16,20,23,13,11,25,17,28,16,15,14,13,23,18,26,29,16,32,13,20,28,24 %N A254763 One half of the fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = A007519(n), n>=1 (primes congruent to 1 mod 8). %C A254763 The corresponding fundamental solution x2(n) of this second class of positive solutions is given in A254762(n). %C A254763 See the comments and the Nagell reference in A254760. %F A254763 A254762(n)^2 - 2*(2*a(n))^2 = A007519(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation. %F A254763 a(n) = A254760(n) - 3*A254761(n), n >= 1. %e A254763 n = 2: 13^2 - 2*(2*4)^2 = 169 - 128 = 41. %e A254763 The smallest positive solution is (x1(2), y1(2)) = (7, 2) from (A254760(2), 2*A254761(2)). %e A254763 See also A254762. %e A254763 a(4) = 11 - 3*2 = 5. %Y A254763 Cf. A007519, A005123, A254762, A254760, 2*A254761. %K A254763 nonn,easy %O A254763 1,1 %A A254763 _Wolfdieter Lang_, Feb 10 2015