A353140 - OEIS

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..37.

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 *)

PROG

(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

CROSSREFS