A352452 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k+1 does not divide n.

0, 0, 0, 2, 4, 4, 0, 6, 0, 8, 8, 10, 0, 12, 12, 10, 16, 16, 16, 18, 4, 16, 20, 22, 16, 8, 24, 26, 20, 28, 8, 30, 32, 32, 32, 34, 0, 36, 36, 34, 32, 40, 8, 42, 36, 40, 44, 46, 16, 48, 32, 50, 52, 52, 16, 38, 48, 56, 56, 58, 0, 60, 60, 58, 64, 64, 64, 66, 68, 64

Offset: 0

Author

Rémy Sigrist, Mar 16 2022

Keywords

• nonn
• base

Comments

The idea is to keep the 1's in the binary expansion of a number whose positions are related in some way to that number.

Examples

			For n = 42:
- 42 = 2^5 + 2^3 + 2^1,
- 5+1 divides 42,
- 3+1 does not divide 42,
- 1+1 divides 42,
- so a(42) = 2^3 = 8.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

See A352449, A352450, A352451, A352458 for similar sequences.

Programs

PARI

a(n) = { my (v=0, m=n, k); while (m, m-=2^k=valuation(m,2); if (n%(k+1), v+=2^k)); v }

Formula

a(n) <= n.