%I #29 Dec 25 2021 09:44:27

%S 0,1,2,3,7,17,27,37,87,137,157,187,247,437,687,787,937,1237,2187,3437,

%T 3937,4687,6187,8437,10937,17187,19687,23437,30937,42187,54687,55687,

%U 85937,98437,117187,154687,210937,223437,273437,278437,304687,429687,492187,585937

%N Record terms of A349664.

%C Terms are the record numbers of solutions for the equation: y^4 = z^2 - x^2.

%H Karl-Heinz Hofmann, <a href="/A349665/a349665.txt">Full table up to y <= 10^12</a>

%e Number of | y | Factorization

%e solutions | | of y

%e ----------+---+--------------

%e 0 | 1 | -

%e 1 | 2 | [2]

%e 2 | 3 | [3]

%e 3 | 4 | [2, 2]

%e 7 | 6 | [2, 3]

%e : : :

%e For more terms with y and factorization of y see link.

%o (PARI) lista(nn) = my(f, r); print1("0, 1, 2"); forstep(n=4, nn, 2, f=factor(n)[, 2]; if(r<f=prod(k=2, #f, 4*f[k]+1)*(4*f[1]-1), print1(", ", (r=f)\2))); \\ _Jinyuan Wang_, Dec 19 2021

%Y Cf. A000290, A000583, A002144, A002145, A271576, A346115, A349663.

%K nonn

%O 1,3

%A _Karl-Heinz Hofmann_, Dec 18 2021

%E More terms from _Jinyuan Wang_, Dec 19 2021