A345290 a(n) is obtained by replacing 2^k in binary expansion of n with Fibonacci(-k-2).

0, -1, 2, 1, -3, -4, -1, -2, 5, 4, 7, 6, 2, 1, 4, 3, -8, -9, -6, -7, -11, -12, -9, -10, -3, -4, -1, -2, -6, -7, -4, -5, 13, 12, 15, 14, 10, 9, 12, 11, 18, 17, 20, 19, 15, 14, 17, 16, 5, 4, 7, 6, 2, 1, 4, 3, 10, 9, 12, 11, 7, 6, 9, 8, -21, -22, -19, -20, -24

Offset

0,3

Comments

This sequence is a variant of A022290; here we consider Fibonacci numbers with negative indices (A039834), there Fibonacci numbers with positive indices (A000045).

After the initial 0, the sequence alternates runs of positive terms and runs of negative terms, the k-th run having 2^(k-1) terms.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Formula

a(n) = A022290(A063695(n)) - A022290(A063694(n)).

a(n) = A022290(n) iff n belongs to A062880.

a(n) = -A022290(n) iff n belongs to A000695.

a(n) = 0 iff n = 0.

a(n) = 1 iff n belongs to A072197.

a(n) = 2 iff n belongs to A080675.

a(n) = -1 iff n belongs to A020989.

a(n) = -2 iff n belongs to A136412.

Example

For n = 3:
- 3 = 2^1 + 2^0,
- so a(3) = A039834(2+1) + A039834(2+0) = 2 - 1 = 1.

Prog

(PARI) a(n) = { my (v=0, e); while (n, n-=2^e=valuation(n, 2); v+=fibonacci(-2-e)); v }

Crossrefs

Cf. A000045, A000695, A020989, A022290, A039834, A062880, A063694, A063695, A072197, A080675, A136412, A345291, A345292.

Sequence in context: A247045 A347354 A361429 * A372619 A330669 A084579

Adjacent sequences: A345287 A345288 A345289 * A345291 A345292 A345293

Keyword

sign,base

Author

Rémy Sigrist, Jun 13 2021

Status

approved