A207079 The only nonunique differences between powers of 3 and 2.

1, 5, 7, 13, 23

Offset: 1

Author

Gottfried Helms, Feb 15 2012

Keywords

• nonn
• bref
• fini
• full

Comments

The sequence is finite, this fact is a theorem in [Bennet2004].

1 = 3-2 = 3^2-2^3 = 2^2-3.

5 = 3^2-2^2 = 2^3-3 = 2^5 - 3^3.

7 = 2^4-3^2 = 3^2 - 2.

13 = 2^4-3 = 2^8 - 3^5.

23 = 3^3 - 2^2 = 2^5 - 3^2.

Links

• M. A. Bennett, Pillai's conjecture revisited, J. Number Theory 98 (2003), 228-235.
• Douglas Edward Iannucci, On duplicate representations as 2^x+3^y for nonnegative integers x and y, arXiv:1907.03347 [math.NT], 2019. Mentions this sequence.

Crossrefs

Cf. A053289, A074981, A076438, A219551.

Formula

A219551(a(n)) > 1. - Jonathan Sondow, Dec 10 2012