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

Author

Rémy Sigrist, Jun 13 2021

Keywords

• sign
• base

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.

Examples

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

Links

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

Crossrefs

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

Programs

PARI

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

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.