A355062 Perfect powers whose digits are in nondecreasing order.

4, 8, 9, 16, 25, 27, 36, 49, 125, 128, 144, 169, 225, 256, 289, 1156, 1225, 1369, 1444, 4489, 6889, 11236, 11449, 13456, 13689, 27889, 33489, 111556, 112225, 113569, 134689, 146689, 344569, 444889, 2666689, 2778889, 11115556, 11122225, 11135569, 11336689

Offset: 1

Author

Jon E. Schoenfield, Jun 16 2022

Keywords

• nonn
• base

Comments

I.e., numbers of the form b^k with b > 1 and k > 1 in whose base-10 expansion no digit is less than the previous digit.

Includes infinite subsequences such as {16, 1156, 111556, 11115556, ...} and {25, 1225, 112225, 11122225, ...}, so the sequence is infinite.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..261

Crossrefs

Cf. A001597, A009994, A355060.

Programs

Mathematica

perfectPowerQ[n_] := GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) Select[Range[10^6], perfectPowerQ[#] && Min[Differences[IntegerDigits[#]]]>-1 &] (* Stefano Spezia, Jul 01 2025 *)

PARI

isok(m) = if (ispower(m), my(d=digits(m)); (d == vecsort(d))); \\ Michel Marcus, Jun 18 2022

Python

from sympy import perfect_power as pp
from itertools import count, islice, combinations_with_replacement as mc
def agen():
    for d in count(1):
        ni = (int("".join(m)) for m in mc("123456789", d))
        yield from filter(pp, ni)
print(list(islice(agen(), 40))) # Michael S. Branicky, Jun 16 2022