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

0, 20, 32, 95, 207, 720, 1152, 1215, 1287, 3420, 3807, 6255, 6407, 7452, 7767, 18095, 23247, 25920, 41472, 43740, 46332, 46647, 69255, 123120, 137052, 174087, 211815, 217935, 225180, 230652, 268272, 279612, 279927, 651420, 836892, 933120, 1416447

Offset

1,2

Comments

Numbers n such that equation 6^x-y^2=n has more than one solution.

Links

Table of n, a(n) for n=1..37.

Example

0=6^(2k)-(6^k)^2, k=1,2,..
20=6^2-4^2=6^3-14^2,
32=6^2-2^2=6^5-88^2,
95=6^3-11^2=6^7-529^2,
207=6^3-3^2=6^4-33^2=6^5-87^2,
720=6^4-24^2=6^5-84^2,
1152=6^4-12^2=6^7-528^2,
1215=6^4-9^2=6^5-81^2,
1287=6^4-3^2=6^6-213^2.

Mathematica

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

Crossrefs

Cf. A051217.

Sequence in context: A333729 A183048 A124665 * A119873 A364307 A075230

Adjacent sequences: A134986 A134987 A134988 * A134990 A134991 A134992

Keyword

nonn

Author

Zak Seidov, Feb 05 2008

Extensions

More terms from Robert G. Wilson v, Feb 09 2008

Status

approved