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

3274, 13453, 13492, 13706, 14726, 15113, 15498, 15528, 52049, 52251, 52330, 52673, 52778, 53478, 53684, 53775, 53972, 54295, 54411, 54598, 54601, 55057, 55449, 55462, 55505, 55512, 55689, 56333, 58066, 58260, 58446, 58453, 58470, 58918, 59266, 59722, 59786

Offset: 1

Author

Alex Ratushnyak, Apr 26 2022

Keywords

• nonn
• base

Comments

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.

Crossrefs

Cf. A031443, A345397, A353139.

Programs

Mathematica

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 *)

Python

from itertools import count, islice
from sympy.utilities.iterables import multiset_permutations
def isbalanced(n): b = bin(n)[2:]; return b.count("0") == b.count("1")
def A031443gen(): yield from (int("1"+"".join(p), 2) for n in count(1) for p in multiset_permutations("0"*n+"1"*(n-1)))
def agen():
    for k in A031443gen():
        if isbalanced(k**2) and isbalanced(k**3):
            yield k
print(list(islice(agen(), 40))) # Michael S. Branicky, Apr 26 2022