A352449 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n = k (where AND denotes the bitwise AND operator).

0, 1, 0, 3, 0, 1, 4, 7, 0, 1, 0, 11, 0, 1, 4, 15, 0, 1, 0, 3, 16, 17, 20, 23, 0, 1, 0, 11, 16, 17, 20, 31, 0, 1, 0, 3, 0, 33, 4, 39, 0, 1, 0, 11, 0, 33, 4, 47, 0, 1, 0, 3, 16, 49, 20, 55, 0, 1, 0, 11, 16, 49, 20, 63, 0, 1, 0, 3, 0, 1, 68, 71, 0, 1, 0, 11, 0, 1

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 belongs to A309274.

Example

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

Prog

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

Crossrefs

See A352450, A352451, A352452, A352458 for similar sequences.

Cf. A309274 (fixed points).

Sequence in context: A106683 A139601 A213191 * A079520 A229001 A208981

Adjacent sequences: A352446 A352447 A352448 * A352450 A352451 A352452

Keyword

nonn,base

Author

Rémy Sigrist, Mar 16 2022

Status

approved