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 A377600 #15 Feb 16 2025 08:34:07 %S A377600 1,3,4,7,12,13,19,21,28,31,39,43,52,57,61,67,73,76,84,91,93,97,103, %T A377600 109,111,124,127,129,133,139,147,151,157,163,172,181,183,193,199,201, %U A377600 211,217,228,237,241,244,247,259,268,271,273,277,283,292,301,307,309,313,327,331,337,343,364 %N A377600 Positive integers D such that the generalized Pell equation X^2 - D Y^2 = -3 is solvable over the integers. %C A377600 Calculated using Dario Alpern's quadratic Diophantine solver, see link. %H A377600 Robin Visser, <a href="/A377600/b377600.txt">Table of n, a(n) for n = 1..10000</a> %H A377600 Dario Alpern, <a href="https://www.alpertron.com.ar/QUAD.HTM">Generic two integer variable equation solver</a>. %H A377600 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>. %e A377600 The first fundamental solutions [x(n), y(n)] are (the first entry gives D(n)=a(n)): %e A377600 [1, [1, 2]], [3, [0, 1]], [4, [1, 1]], [7, [2, 1]], [12, [3, 1]], [13, [7, 2]], [19, [4, 1]], [21, [9, 2]], [28, [5, 1]], [31, [11, 2]], [39, [6, 1]], [43, [13, 2]], [52, [7, 1]], [57, [15, 2]], [61, [5639, 722]], [67, [8, 1]], [73, [17, 2]], [76, [61, 7]], [84, [9, 1]], [91, [19, 2]], [93, [135, 14]], [97, [847, 86]], [103, [10, 1]], [109, [1399, 134]], [111, [21, 2]], [124, [11, 1]], [127, [293, 26]], [129, [159, 14]], [133, [23, 2]], [139, [224, 19]], [147, [12, 1]], [151, [86, 7]], [157, [25, 2]], [163, [932, 73]], [172, [13, 1]], [181, [11262809, 837158]], [183, [27, 2]], [193, [189743, 13658]], [199, [14, 1]], ... %o A377600 (Python) %o A377600 from itertools import count, islice %o A377600 from sympy.solvers.diophantine.diophantine import diop_DN %o A377600 def A377600_gen(startvalue=1): # generator of terms >= startvalue %o A377600 return filter(lambda d:len(diop_DN(d,-3)), count(max(startvalue,1))) %o A377600 A377600_list = list(islice(A377600_gen(),63)) # _Chai Wah Wu_, Nov 03 2024 %Y A377600 Cf. A031396, A244819, A261246, A377607. %K A377600 nonn %O A377600 1,2 %A A377600 _Robin Visser_, Nov 02 2024