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 A336787 #38 Feb 27 2021 21:48:46 %S A336787 2,3,5,39,59,477,2175,41571,127539,340551,15732537,221272626669, %T A336787 2700614460969,66944775830061,616049024759241,6245844517335369, %U A336787 13085071811371140879,43795350588094552821,63464174140920940599,633160367499665048108061 %N A336787 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = 2, where D is a prime number. %C A336787 Analogous to A033315 for x^2 - D*y^2 = 1, and D required to be prime. The x values incrementally largest for x^2 - D*y^2 = 2. D values appear in sequence A336786. %H A336787 Christine Patterson, <a href="/A336787/a336787.txt">Sage Program</a> %e A336787 For D=31, the least x for which x^2 - Dy^2 = 2 has a solution is 39. The next prime, D, for which x^2 - Dy^2 = 2 has a solution is 47, but the smallest x in this case is 7, which is less than 39. The next prime, D, after 47 for which x^2 - Dy^2 = 2 has a solution is 71 and the least x for which it has a solution is x=59, which is larger than 39, a new record value, so 71 is a term of A336786 and 59 is the corresponding term of this sequence. 47 is not a term of A336786 because the least x for which x^2 - 47*y^2 = 2 has a solution is not a record value. %e A336787 From _Jon E. Schoenfield_, Feb 24 2021: (Start) %e A336787 Primes D for which the equation x^2 - D*y^2 = 2 has integer solutions begin 2, 7, 23, 31, 47, 71, 79, 103, ...; at those values of D, the minimal x values satisfying the equation x^2 - D*y^2 = 2 begin as follows: %e A336787 . %e A336787 x values satisfying minimal %e A336787 D x^2 - D*y^2 = 2 x value record %e A336787 --- --------------------------- ------- ------ %e A336787 2 2, 10, 58, 338, 1970, ... 2 * %e A336787 7 3, 45, 717, 11427, ... 3 * %e A336787 23 5, 235, 11275, 540965, ... 5 * %e A336787 31 39, 118521, 360303801, ... 39 * %e A336787 47 7, 665, 63833, 6127303, ... 7 %e A336787 71 59, 410581, 2857643701, ... 59 * %e A336787 79 9, 1431, 228951, ... 9 %e A336787 103 477, 217061235, ... 477 * %e A336787 ... %e A336787 The record high minimal values of x (marked with asterisks) are the terms of this sequence. The corresponding values of D are the terms of A336786. (End) %Y A336787 Cf. A033315, A336786. %K A336787 nonn %O A336787 1,1 %A A336787 _Christine Patterson_, Aug 05 2020 %E A336787 a(1)=2 inserted and Example section edited by _Jon E. Schoenfield_, Feb 24 2021