A385351 Perfect powers whose digits are all powers of the same single-digit base.

1, 4, 8, 9, 16, 81, 121, 128, 144, 441, 484, 841, 1331, 1444, 8281, 11881, 14884, 28224, 48841, 114244, 128881, 142884, 221841, 228484, 848241, 1121481, 1281424, 1418481, 2184484, 2214144, 8282884, 9393931, 11142244, 11282881, 18241441, 18818244, 18844281, 21242881

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Example

841 is a term since it is equal to 29^2 and its digits are all powers of 2: 8 = 2^3, 4 = 2^2, and 1 = 2^0;
1331 is a term since it is equal to 11^3 and its digits are all powers of 3: 1 = 3^0 and 3 = 3^1.

Mathematica

perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *)
nterms=20; list={}; len=0; n=1; While[len <=nterms, If[perfectPowerQ[n] &&(SubsetQ[{0}, dig=IntegerDigits[n]] || SubsetQ[{1, 2, 4, 8}, dig] || SubsetQ[{1, 3, 9}, dig] || SubsetQ[{1, 5}, dig] || SubsetQ[{1, 6}, dig] || SubsetQ[{1, 7}, dig]), AppendTo[list, n]; len++]; n++]; list

Crossrefs

Cf. A001597, A385324 (supersequence).

Sequence in context: A202271 A334858 A162898 * A257009 A071592 A089765

Adjacent sequences: A385348 A385349 A385350 * A385352 A385353 A385354

Keyword

nonn,base

Author

Stefano Spezia, Jun 26 2025

Status

approved