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 A341085 #13 Feb 20 2021 23:09:45 %S A341085 5,29,61,109,181,661,1021,1549,2161,2389,3169,3469,4909,5581,8929, %T A341085 9601,9949,12841,13381,14029,17029,21169,24709,25309,28729,31249, %U A341085 32869,34549,35149,39901,40429,43801,48049,49009,56401,56701,62701,63541,70141,86269 %N A341085 Value of prime number D for incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -5. %H A341085 Christine Patterson, <a href="/A341085/a341085.txt">COCALC (Sage) Program</a> %e A341085 For D=29, the least positive y for which x^2 - D*y^2 = -5 has a solution is 3. The next prime, D, for which x^2 - D*y^2 = -5 has a solution is 41, but the smallest positive y in this case is 1, which is less than the previous record y, 3. So, 41 is not a term. %e A341085 The next prime, D, after 41 for which x^2 - D*y^2 = -5 has a solution is 61 and the least positive y for which it has a solution is y=21, which is larger than 3, so it is a new record y value. So 61 is a term of this sequence and 21 is the corresponding term of A341086. %e A341085 From _Jon E. Schoenfield_, Feb 20 2021: (Start) %e A341085 As D runs through the primes, the minimal y values satisfying the equation x^2 - D*y^2 = -5 begin as follows: %e A341085 . %e A341085 y values satisfying minimal %e A341085 D x^2 - D*y^2 = -5 y value record %e A341085 -- -------------------- ------- ------ %e A341085 2 (none) %e A341085 3 (none) %e A341085 5 1, 9, 161, 2889, ... 1 * %e A341085 7 (none) %e A341085 11 (none) %e A341085 13 (none) %e A341085 17 (none) %e A341085 19 (none) %e A341085 23 (none) %e A341085 29 3, 283, 58523, ... 3 * %e A341085 31 (none) %e A341085 37 (none) %e A341085 41 1, 129, 3969, ... 1 %e A341085 43 (none) %e A341085 47 (none) %e A341085 51 (none) %e A341085 53 (none) %e A341085 59 (none) %e A341085 61 21, 3447309, ... 21 * %e A341085 ... %e A341085 The record high minimal values of y (marked with asterisks) are the terms of A341086. The corresponding values of D are the terms of this sequence. (End) %Y A341085 Cf. A033316 (analogous for x^2 - D*y^2 = 1), A341083 (similar sequence for x's), A341086. %K A341085 nonn %O A341085 1,1 %A A341085 _Christine Patterson_, Feb 13 2021 %E A341085 a(1)=5 inserted by _Jon E. Schoenfield_, Feb 20 2021