A352451 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k+1 divides n.

0, 1, 2, 1, 0, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 5, 0, 1, 2, 1, 16, 5, 2, 1, 8, 17, 2, 1, 8, 1, 22, 1, 0, 1, 2, 1, 36, 1, 2, 5, 8, 1, 34, 1, 8, 5, 2, 1, 32, 1, 18, 1, 0, 1, 38, 17, 8, 1, 2, 1, 60, 1, 2, 5, 0, 1, 2, 1, 0, 5, 66, 1, 8, 1, 2, 1, 8, 65, 6, 1, 16, 1

Offset

0,3

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Formula

a(n) <= n.

Example

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) = 2^5 + 2^1 = 34.

Prog

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

Crossrefs

See A352449, A352450, A352452, A352458 for similar sequences.

Sequence in context: A302978 A108723 A291584 * A349618 A321615 A011126

Adjacent sequences: A352448 A352449 A352450 * A352452 A352453 A352454

Keyword

nonn,base

Author

Rémy Sigrist, Mar 16 2022

Status

approved