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A134989 Numbers expressible in more than one way as 6^x-y^2.

%I A134989 #7 Aug 10 2025 04:18:49
%S A134989 0,20,32,95,207,720,1152,1215,1287,3420,3807,6255,6407,7452,7767,
%T A134989 18095,23247,25920,41472,43740,46332,46647,69255,123120,137052,174087,
%U A134989 211815,217935,225180,230652,268272,279612,279927,651420,836892,933120,1416447
%N A134989 Numbers expressible in more than one way as 6^x-y^2.
%C A134989 Numbers n such that equation 6^x-y^2=n has more than one solution.
%e A134989 0=6^(2k)-(6^k)^2, k=1,2,..
%e A134989 20=6^2-4^2=6^3-14^2,
%e A134989 32=6^2-2^2=6^5-88^2,
%e A134989 95=6^3-11^2=6^7-529^2,
%e A134989 207=6^3-3^2=6^4-33^2=6^5-87^2,
%e A134989 720=6^4-24^2=6^5-84^2,
%e A134989 1152=6^4-12^2=6^7-528^2,
%e A134989 1215=6^4-9^2=6^5-81^2,
%e A134989 1287=6^4-3^2=6^6-213^2.
%t A134989 lst = {}; Do[ t = 6^x - y^2; If[t < 10^7/7, AppendTo[lst, t]], {x, 185}, {y, (a = Floor@Sqrt[6^x - 10^7]; If[Element[a, Reals], a, 0]), Floor@Sqrt[6^x]}]; lst = Sort@lst; lsu = {}; Do[ If[lst[[n]] == lst[[n + 1]], AppendTo[lsu, lst[[n]]]], {n, -1 + Length@lst}]; Union@lsu (* _Robert G. Wilson v_, Feb 09 2008 *)
%Y A134989 Cf. A051217.
%K A134989 nonn
%O A134989 1,2
%A A134989 _Zak Seidov_, Feb 05 2008
%E A134989 More terms from _Robert G. Wilson v_, Feb 09 2008