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

Author

Stefano Spezia, Jun 26 2025

Keywords

• nonn
• base

Examples

			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.
		

Crossrefs

Cf. A001597, A385324 (supersequence).

Programs

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