A023057 (Apparently) not the difference between adjacent perfect powers (A001597, integers of form a^b, a >= 1, b >= 2).

6, 14, 22, 29, 31, 34, 42, 44, 46, 50, 52, 54, 58, 62, 64, 66, 70, 72, 78, 82, 84, 86, 88, 90, 91, 96, 98, 102, 105, 110, 111, 114, 117, 118, 120, 122, 124, 126, 130, 132, 134, 136, 140, 142, 153, 156, 158, 160, 162, 164, 165, 172, 176, 177, 178, 179, 181, 182, 188, 190

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• nice

Comments

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

References

• G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..4479
• Alf van der Poorten, Remarks on the sequence of 'perfect' powers.

Crossrefs

Cf. A001597 (perfect powers), A023055 (complement). See also A074980, A074981, A077286.

Programs

Mathematica

pp = Union[ Join[{1}, Flatten[ Table[n^i, {n, 2, Sqrt[10^12]}, {i, 2, Log[n, 10^12]}]]]]; l = Length[pp]; d = Sort[Take[pp, -l + 1] - Take[pp, l - 1]]; Complement[ Table[i, {i, 1, 200}], Take[ Union[d], 200]] (* Robert G. Wilson v *)