A355060 Perfect powers whose digits are in strictly increasing order.

4, 8, 9, 16, 25, 27, 36, 49, 125, 128, 169, 256, 289, 1369, 13456, 13689, 134689

Offset: 1

Author

Jon E. Schoenfield, Jun 16 2022

Keywords

• nonn
• base
• fini
• full

Comments

I.e., numbers of the form b^k with b > 1 and k > 1 in whose base-10 expansion each digit is greater than the previous digit.

Crossrefs

Cf. A001597, A009993, A355062.

Programs

Mathematica

perfectPowerQ[n_] := GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) Select[Range[135000], perfectPowerQ[#] && AllTrue[Differences[IntegerDigits[#]],Positive] &] (* Stefano Spezia, Jul 01 2025 *)