A351565 Odd part of Kimberling's paraphrases: a(n) = A000265(A003602(n)).

1, 1, 1, 1, 3, 1, 1, 1, 5, 3, 3, 1, 7, 1, 1, 1, 9, 5, 5, 3, 11, 3, 3, 1, 13, 7, 7, 1, 15, 1, 1, 1, 17, 9, 9, 5, 19, 5, 5, 3, 21, 11, 11, 3, 23, 3, 3, 1, 25, 13, 13, 7, 27, 7, 7, 1, 29, 15, 15, 1, 31, 1, 1, 1, 33, 17, 17, 9, 35, 9, 9, 5, 37, 19, 19, 5, 39, 5, 5, 3, 41, 21, 21, 11, 43, 11, 11, 3, 45, 23, 23, 3, 47

Offset: 1

Author

Antti Karttunen, Mar 27 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000265, A003602, A023758 (gives the positions of 1's after its initial zero-term).

Cf. also A336698, A336699.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A351565(n) = A000265(1+A000265(n));

Python

def A351565(n): return (m:=1+(n>>(~n&n-1).bit_length()))>>(~m&m-1).bit_length()  # Chai Wah Wu, Jan 03 2024

Formula

a(n) = A000265(A003602(n)) = A000265(1+A000265(n)).