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

%I A385351 #15 Jun 27 2025 20:59:53
%S A385351 1,4,8,9,16,81,121,128,144,441,484,841,1331,1444,8281,11881,14884,
%T A385351 28224,48841,114244,128881,142884,221841,228484,848241,1121481,
%U A385351 1281424,1418481,2184484,2214144,8282884,9393931,11142244,11282881,18241441,18818244,18844281,21242881
%N A385351 Perfect powers whose digits are all powers of the same single-digit base.
%e A385351 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;
%e A385351 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.
%t A385351 perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *)
%t A385351 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
%Y A385351 Cf. A001597, A385324 (supersequence).
%K A385351 nonn,base
%O A385351 1,2
%A A385351 _Stefano Spezia_, Jun 26 2025