A352458 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, 1, 2, 1, 4, 5, 2, 1, 8, 1, 2, 1, 12, 5, 2, 1, 16, 17, 18, 17, 4, 5, 2, 1, 24, 17, 18, 17, 12, 5, 2, 1, 32, 1, 34, 1, 4, 5, 2, 1, 40, 1, 34, 1, 12, 5, 2, 1, 48, 17, 50, 17, 4, 5, 2, 1, 56, 17, 50, 17, 12, 5, 2, 1, 64, 65, 2, 1, 4, 5, 2, 1, 72, 65, 2, 1, 12

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 with equality iff n belongs to A335702.

a(n) = n - A309274(n).

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

Prog

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

Crossrefs

See A352449, A352450, A352451, A352452 for similar sequences.

Cf. A335702 (fixed points).

Sequence in context: A248666 A162407 A368608 * A132741 A072436 A247503

Adjacent sequences: A352455 A352456 A352457 * A352459 A352460 A352461

Keyword

nonn,base

Author

Rémy Sigrist, Mar 17 2022

Status

approved