A023055 (Apparently) differences between adjacent perfect powers (integers of form a^b, a >= 1, b >= 2).

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 32, 33, 35, 36, 37, 38, 39, 40, 41, 43, 45, 47, 48, 49, 51, 53, 55, 56, 57, 59, 60, 61, 63, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 83, 85, 87, 89, 92, 93, 94, 95, 97, 99, 100

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• hard

Comments

Catalan's conjecture (now a theorem) is that 1 occurs just once as a difference, between 8 and 9.

Links

• Alf van der Poorten, Remarks on the sequence of 'perfect' powers

Crossrefs

Cf. A001597, A023057.

Cf. A189117 (conjectured number of pairs of consecutive perfect powers differing by n).