A023055 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..73.

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).

Sequence in context: A047595 A079298 A263715 * A359528 A365819 A359908

Adjacent sequences: A023052 A023053 A023054 * A023056 A023057 A023058

KEYWORD

nonn,hard

AUTHOR

David W. Wilson

STATUS

approved