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 A254935 #23 May 23 2025 01:17:28
%S A254935 3,5,7,7,7,9,9,11,11,11,13,15,13,13,17,15,17,19,15,17,21,17,17,21,19,
%T A254935 23,19,19,21,23,25,21,21,27,23,29,23,23,23,23,27,25,29,31,25,33,25,27,
%U A254935 31,29,35,27,27,31,35,33,29,35,29,31,35,31,37,31,31,33,31,41,43,39,35,37,33,41,33,35,41
%N A254935 Fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A007519(n), n>=1 (primes congruent to 1 mod 8).
%C A254935 For the corresponding term x1(n) see A254934(n).
%C A254935 See A254934 also for the Nagell reference.
%C A254935 The least positive y solutions (that is the ones of the first class) for the primes +1 and -1 (mod 8) together (including prime 2) are given in A255246.
%H A254935 M. F. Hasler, <a href="/A254935/b254935.txt">Table of n, a(n) for n = 1..1000</a>, May 22 2025
%F A254935 A254934(n)^2 - 2*a(n)^2 = -A007519(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.
%e A254935 See A254934.
%e A254935 n = 3: 5^2 - 2*7^2 = 25 - 98 = -73.
%o A254935 (PARI) apply( {A254935(n, p=A007519(n))=sqrtint((A254934(,p)^2+p)\2)}, [1..77]) \\ _M. F. Hasler_, May 22 2025
%Y A254935 Cf. A007519 (primes == 1 mod 8), A005123 (8k+1 is prime).
%Y A254935 Cf. A254934 (corresponding x1 values), A254936 (x2 values), A254937 (y2 values), A254938 (same for primes == 7 mod 8), A255232 (y2 values, halved).
%K A254935 nonn,easy
%O A254935 1,1
%A A254935 _Wolfdieter Lang_, Feb 18 2015
%E A254935 More terms from _M. F. Hasler_, May 22 2025