A379448 a(n) is the number of ones in the binary expansion of n^(n^n).

1, 1, 30, 1, 3683, 36635, 1156050, 1, 614037343, 11609679812, 493508438640

Offset

1,3

Links

Table of n, a(n) for n=1..11.

Formula

a(2^k) = 1. - Chai Wah Wu, Dec 24 2024

Probably a(n) = n^n * log(A000265(n))/log(4) + O(n^(n/2)) by analogy with the Law of the Iterated Logarithm. - Charles R Greathouse IV, Dec 27 2024

Mathematica

Table[DigitCount[n^n^n, 2, 1], {n, 9}] (* James C. McMahon, Dec 26 2024 *)

Prog

(PARI) a379448(n) = hammingweight(n^n^n)
(PARI) a(n)=hammingweight((n>>valuation(n, 2))^n^n) \\ Charles R Greathouse IV, Dec 26 2024
(Python)
def A379448(n): return 1 if n.bit_count()==1 else (n**n**n).bit_count() # Chai Wah Wu, Dec 24 2024

Crossrefs

Cf. A000120, A002488, A214561, A379446, A379447.

Sequence in context: A040927 A040928 A040929 * A040892 A040893 A040891

Adjacent sequences: A379445 A379446 A379447 * A379449 A379450 A379451

Keyword

nonn,base,more

Author

Hugo Pfoertner, Dec 24 2024

Extensions

a(11) from Markus Sigg, Dec 27 2024

Status

approved