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

49, 8677, 53543, 141169, 202055, 755917

Offset: 1

Author

Alex Ratushnyak, May 02 2022

Keywords

• nonn
• base
• hard
• more

Crossrefs

Cf. A031443, A353139.

Programs

Mathematica

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 *)

Python

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

Extensions

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