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

1,1

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

Prog

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

Crossrefs

Cf. A001597, A009994, A355060.

Sequence in context: A195942 A125643 A002760 * A355060 A115651 A062559

Adjacent sequences: A355059 A355060 A355061 * A355063 A355064 A355065

Keyword

nonn,base

Author

Jon E. Schoenfield, Jun 16 2022

Status

approved