A085634 Numbers of the form 2^a + 3^b = 2^c + 3^d for nonnegative a, b, c, d and a <> c.

5, 11, 17, 35, 259

Offset

1,1

Comments

No more terms < 10^4000. - David Wasserman, Feb 07 2005

Links

Table of n, a(n) for n=1..5.

Douglas Edward Iannucci, On duplicate representations as 2^x+3^y for nonnegative integers x and y, arXiv:1907.03347 [math.NT], 2019.

Example

a(5) = 256 + 3 = 2^8 + 3^1 = 259 = 16 + 243 = 2^4 + 3^5.

Mathematica

(* Max exponent 8 is sufficient to get all known solutions *)
f[_] = 0; Reap[Do[n = 2^a + 3^b; f[n] = f[n] + 1; If[f[n] == 1, ab[n] = {a, b}, If[f[n] >= 2, Print[HoldForm[2^x + 3^y] /. Thread[{x, y} -> ab[n]], " = ", HoldForm[2^x + 3^y] /. Thread[{x, y} -> {a, b}], " = ", n]; Sow[n]]], {a, 0, 8}, {b, 0, 8}]][[2, 1]] // Union (* Jean-François Alcover, Apr 29 2014 *)

Crossrefs

Sequence in context: A155030 A030468 A277290 * A157478 A297583 A356756

Adjacent sequences: A085631 A085632 A085633 * A085635 A085636 A085637

Keyword

nonn,fini,full

Author

Frank Ellermann, Jul 11 2003

Status

approved