A353139 -id:A353139 - cp's OEIS frontend

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

Alex Ratushnyak, Apr 26 2022

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.

Cf. A031443, A345397, A353139.

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 *)

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

A351598 Digitally balanced numbers b (A031443) such that b^b is also digitally balanced.

Original entry on oeis.org

49, 8677, 53543, 141169, 202055, 755917

Offset: 1

Alex Ratushnyak, May 02 2022

Cf. A031443, A353139.

balQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ @ (m = Length @ d) && Count[d, 1] == m/2]; Select[Range[10000], balQ[#] && balQ[#^#] &] (* Amiram Eldar, May 03 2022 *)

from itertools import count, islice
def isdb(n): b = bin(n)[2:]; return b.count("0") == b.count("1")
def agen(): yield from (b for b in count(1) if isdb(b) and isdb(b**b))
print(list(islice(agen(), 2))) # Michael S. Branicky, Jun 12 2022

a(4)-a(6) from Amiram Eldar, May 03 2022

A372147 Numbers k for which k and k^2 are digitally balanced numbers in base 3 (A049354).

Original entry on oeis.org

500, 544, 550, 552, 588, 622, 307172, 307402, 307888, 308920, 309480, 309522, 309604, 310348, 310422, 310658, 310754, 310964, 310974, 310980, 311206, 311214, 311342, 311466, 311582, 311788, 311790, 312050, 312070, 312100, 313022, 313050, 313336, 313502, 313512

Offset: 1

Marius A. Burtea, May 23 2024

			500 = 200112_3 and 500^2 = 250000 =110200221021_3, so 500 is a term.
544 = 202011_3 and 544^2 = 295936 =120000221121_3, so 544 is a term.

Cf. A049354, A353139, A353140.

bal:=func; [n:n in [1..320000]|bal(n) and bal(n*n)];

balQ[n_, b_] := MinMax@ Differences@ DigitCount[n, b] == {0, 0}; Select[Range[320000], balQ[#, 3] && balQ[#^2, 3] &] (* Amiram Eldar, Jun 03 2024 *)

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

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A351598 Digitally balanced numbers b (A031443) such that b^b is also digitally balanced.

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A372147 Numbers k for which k and k^2 are digitally balanced numbers in base 3 (A049354).

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