Conjectured sorted differences between adjacent powers.
1, 2, 3, 3, 4, 4, 4, 5, 7, 7, 8, 9, 9, 9, 10, 11, 11, 12, 13, 13, 13, 15, 15, 16, 17, 17, 17, 17, 17, 18, 18, 19, 19, 19, 20, 21, 23, 24, 24, 25, 26, 26, 27, 28, 28, 28, 30, 32, 33, 35, 35, 36, 37, 38, 39, 39, 39, 40, 41, 43, 45, 47, 47, 47, 48, 49, 49, 51, 53, 53
1
Powers up to 10^17 were computed to create this sequence. Sequence S000538 gives the locations of these terms in the list of powers A001597. For instance, the second 3 occurs at position 15 in the list of powers: 125, which is followed by 128.
T. D. Noe, Plot of 70 terms
(Mma) nn = 10^12; mx = Floor[Log[2, nn]]; s = Union[Flatten[Table[Table[i^k, {i, nn^(1/k)}], {k, 2, mx}]]]; d = Differences[s]; Take[Sort[d], 70]
Cf. A001597, A189117, S000538.
nonn,hard
T. D. Noe, Mar 12 2015