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A353140 Digitally balanced numbers (A031443) whose squares and cubes are also digitally balanced.

%I A353140 #15 Apr 28 2022 07:54:54
%S A353140 3274,13453,13492,13706,14726,15113,15498,15528,52049,52251,52330,
%T A353140 52673,52778,53478,53684,53775,53972,54295,54411,54598,54601,55057,
%U A353140 55449,55462,55505,55512,55689,56333,58066,58260,58446,58453,58470,58918,59266,59722,59786
%N A353140 Digitally balanced numbers (A031443) whose squares and cubes are also digitally balanced.
%C A353140 Numbers x such that x, x^2 and x^3 are terms of A031443, that is, have the same number of 0's as 1's in their binary representations.
%t A353140 balQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ @ (m = Length @ d) && Count[d, 1] == m/2]; Select[Range[60000], balQ[#] && balQ[#^2] && balQ[#^3] &] (* _Amiram Eldar_, Apr 26 2022 *)
%o A353140 (Python)
%o A353140 from itertools import count, islice
%o A353140 from sympy.utilities.iterables import multiset_permutations
%o A353140 def isbalanced(n): b = bin(n)[2:]; return b.count("0") == b.count("1")
%o A353140 def A031443gen(): yield from (int("1"+"".join(p), 2) for n in count(1) for p in multiset_permutations("0"*n+"1"*(n-1)))
%o A353140 def agen():
%o A353140     for k in A031443gen():
%o A353140         if isbalanced(k**2) and isbalanced(k**3):
%o A353140             yield k
%o A353140 print(list(islice(agen(), 40))) # _Michael S. Branicky_, Apr 26 2022
%Y A353140 Cf. A031443, A345397, A353139.
%K A353140 nonn,base
%O A353140 1,1
%A A353140 _Alex Ratushnyak_, Apr 26 2022