Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Nov 04 2024 01:41:33
%S 1,6,13,22,33,46,61,69,73,78,94,97,109,118,141,157,166,177,181,193,
%T 213,214,222,241,249,253,262,277,286,313,321,334,337,358,366,382,393,
%U 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 Positive integers D such that the generalized Pell equation X^2 - D Y^2 = 3 is solvable over the integers.
%C Calculated using Dario Alpern's quadratic Diophantine solver, see link.
%H Robin Visser, <a href="/A377607/b377607.txt">Table of n, a(n) for n = 1..10000</a>
%H Dario Alpern, <a href="https://www.alpertron.com.ar/QUAD.HTM">Generic two integer variable equation solver</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>.
%e The first fundamental solutions [x(n), y(n)] are (the first entry gives D(n)=a(n)):
%e [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 (Python)
%o from itertools import count, islice
%o from sympy.solvers.diophantine.diophantine import diop_DN
%o def A377607_gen(startvalue=1): # generator of terms >= startvalue
%o return filter(lambda d:len(diop_DN(d,3)), count(max(startvalue,1)))
%o A377607_list = list(islice(A377607_gen(),61)) # _Chai Wah Wu_, Nov 03 2024
%Y Cf. A031396, A243655, A261246, A377600.
%K nonn
%O 1,2
%A _Robin Visser_, Nov 02 2024