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 A377607 #14 Feb 16 2025 08:34:07 %S A377607 1,6,13,22,33,46,61,69,73,78,94,97,109,118,141,157,166,177,181,193, %T A377607 213,214,222,241,249,253,262,277,286,313,321,334,337,358,366,382,393, %U A377607 397,409,421,429,433,438,454,457,478,481,501,502,517,526,537,541,573,598,601,613,622,649,654,661 %N A377607 Positive integers D such that the generalized Pell equation X^2 - D Y^2 = 3 is solvable over the integers. %C A377607 Calculated using Dario Alpern's quadratic Diophantine solver, see link. %H A377607 Robin Visser, <a href="/A377607/b377607.txt">Table of n, a(n) for n = 1..10000</a> %H A377607 Dario Alpern, <a href="https://www.alpertron.com.ar/QUAD.HTM">Generic two integer variable equation solver</a>. %H A377607 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>. %e A377607 The first fundamental solutions [x(n), y(n)] are (the first entry gives D(n)=a(n)): %e A377607 [1, [2, 1]], [6, [3, 1]], [13, [4, 1]], [22, [5, 1]], [33, [6, 1]], [46, [7, 1]], [61, [8, 1]], [69, [108, 13]], [73, [94, 11]], [78, [9, 1]], [94, [223, 23]], [97, [10, 1]], [109, [9532, 913]], [118, [11, 1]], [141, [12, 1]], [157, [289580, 23111]], [166, [13, 1]], [177, [306, 23]], [181, [148, 11]], [193, [14, 1]], ... %o A377607 (Python) %o A377607 from itertools import count, islice %o A377607 from sympy.solvers.diophantine.diophantine import diop_DN %o A377607 def A377607_gen(startvalue=1): # generator of terms >= startvalue %o A377607 return filter(lambda d:len(diop_DN(d,3)), count(max(startvalue,1))) %o A377607 A377607_list = list(islice(A377607_gen(),61)) # _Chai Wah Wu_, Nov 03 2024 %Y A377607 Cf. A031396, A243655, A261246, A377600. %K A377607 nonn %O A377607 1,2 %A A377607 _Robin Visser_, Nov 02 2024