A340706 Difference between upper and lower member of a pair of adjacent perfect powers A340700 and A340701, both with exponents > 2.

5, 17, 3, 13, 24, 35, 10, 28, 270, 631, 95, 443, 531, 440, 1487, 1934, 503, 8138, 6276, 12311, 16911, 33892, 11573, 17000, 3807, 45197, 30753, 31457, 65170, 105597, 127209, 206808, 109516, 139456, 377711, 530040, 561600, 690742, 952332, 457704, 671064, 353107

Offset: 1

Author

Hugo Pfoertner, Jan 16 2021

Keywords

• nonn

Comments

The differences are expected to be bounded below by the Lang-Waldschmidt conjecture (see Waldschmidt 2013, p. 6, Conjecture 6).

Examples

			See A340700.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..1670
• Michel Waldschmidt, Lecture on the abc conjecture and some of its consequences, Abdus Salam School of Mathematical Sciences (ASSMS), Lahore, 6th World Conference on 21st Century Mathematics 2013.

Crossrefs

Cf. A001597, A076467, A340700, A340701, A340702, A340703, A340704, A340705.

Formula

a(n) = A340701(n) - A340700(n).