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

1,1

Comments

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

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.

Formula

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

Example

See A340700.

Crossrefs

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

Sequence in context: A092679 A277534 A090592 * A093558 A170866 A337031

Adjacent sequences: A340703 A340704 A340705 * A340707 A340708 A340709

Keyword

nonn

Author

Hugo Pfoertner, Jan 16 2021

Status

approved