A353139 Digitally balanced numbers (A031443) whose squares are also digitally balanced.

212, 781, 794, 806, 817, 838, 841, 844, 865, 2962, 3101, 3130, 3171, 3178, 3185, 3213, 3219, 3226, 3269, 3274, 3335, 3353, 3354, 3356, 3370, 3378, 3490, 3496, 3521, 3528, 3595, 3597, 3606, 3610, 3626, 3651, 3672, 3718, 3777, 11797, 11798, 11850, 11938, 12049

Offset

1,1

Comments

Numbers x such that both x and x^2 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..44.

Mathematica

balQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ @ (m = Length @ d) && Count[d, 1] == m/2]; Select[Range[12000], balQ[#] && balQ[#^2] &] (* 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):
            yield k
print(list(islice(agen(), 40))) # Michael S. Branicky, Apr 26 2022

Crossrefs

Cf. A031443, A345397.

Sequence in context: A158794 A204364 A235180 * A114880 A348831 A200433

Adjacent sequences: A353136 A353137 A353138 * A353140 A353141 A353142

Keyword

nonn,base

Author

Alex Ratushnyak, Apr 26 2022

Status

approved