A330569 a(n) = 1 if n is odd, otherwise a(n) = 2^(v-1)+1 where v is the 2-adic valuation of n (A007814(n)).

1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 9, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 17, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 9, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 33, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 9, 1, 2, 1, 3, 1

Offset: 1

Author

N. J. A. Sloane, Jan 07 2020

Keywords

• nonn
• easy

Comments

Conjecture: a(n) is the height of the bottom region in column n of the Conant gasket in A328078.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007814, A328078, A006519 A040001, A140670.

Programs

Mathematica

a[n_] := If[OddQ[n], 1, 1 + 2^(IntegerExponent[n, 2] - 1)]; Array[a, 100] (* Amiram Eldar, Aug 30 2024 *)

PARI

a(n) = if(n % 2, 1, 1 + 1 << (valuation(n, 2) - 1)); \\ Amiram Eldar, Aug 30 2024

Python

def A330569(n): return 1+(0 if n&1 else 1<<(~n & n-1).bit_length()-1) # Chai Wah Wu, Jul 01 2022

Formula

a(n) = (A006519(n) + A040001(n))/2. - Ridouane Oudra, Jul 30 2025