A353139 - OEIS

%I #15 Apr 28 2022 07:48:58

%S 212,781,794,806,817,838,841,844,865,2962,3101,3130,3171,3178,3185,

%T 3213,3219,3226,3269,3274,3335,3353,3354,3356,3370,3378,3490,3496,

%U 3521,3528,3595,3597,3606,3610,3626,3651,3672,3718,3777,11797,11798,11850,11938,12049

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

%C 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.

%t 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 *)

%o (Python)

%o from itertools import count, islice

%o from sympy.utilities.iterables import multiset_permutations

%o def isbalanced(n): b = bin(n)[2:]; return b.count("0") == b.count("1")

%o 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 def agen():

%o     for k in A031443gen():

%o         if isbalanced(k**2):

%o             yield k

%o print(list(islice(agen(), 40))) # _Michael S. Branicky_, Apr 26 2022

%Y Cf. A031443, A345397.

%K nonn,base

%O 1,1

%A _Alex Ratushnyak_, Apr 26 2022