A352450 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n > 0 (where AND denotes the bitwise AND operator).

0, 0, 0, 2, 0, 0, 4, 6, 0, 8, 8, 10, 0, 8, 12, 14, 0, 0, 0, 2, 16, 16, 20, 22, 0, 8, 8, 10, 16, 24, 28, 30, 0, 32, 0, 34, 32, 32, 36, 38, 0, 40, 8, 42, 32, 40, 44, 46, 0, 32, 0, 34, 48, 48, 52, 54, 0, 40, 8, 42, 48, 56, 60, 62, 0, 0, 64, 66, 64, 64, 68, 70, 0

Offset

0,4

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 with equality iff n = 0.

Example

For n = 42:
- 42 = 2^5 + 2^3 + 2^1,
- 42 AND 5 = 0,
- 42 AND 3 = 2 > 0,
- 42 AND 1 = 0,
- so a(42) = 2^3 = 8.

Prog

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

Crossrefs

See A352449, A352451, A352452, A352458 for similar sequences.

Sequence in context: A282551 A333706 A056676 * A098699 A021837 A236934

Adjacent sequences: A352447 A352448 A352449 * A352451 A352452 A352453

Keyword

nonn,base

Author

Rémy Sigrist, Mar 16 2022

Status

approved