A356399 a(n) is the smallest term (in absolute value) in the negaFibonacci representation of n.

1, 2, 1, -1, 5, 1, 2, 1, -1, -3, 1, -1, 13, 1, 2, 1, -1, 5, 1, 2, 1, -1, -3, 1, -1, -8, 1, 2, 1, -1, -3, 1, -1, 34, 1, 2, 1, -1, 5, 1, 2, 1, -1, -3, 1, -1, 13, 1, 2, 1, -1, 5, 1, 2, 1, -1, -3, 1, -1, -8, 1, 2, 1, -1, -3, 1, -1, -21, 1, 2, 1, -1, 5, 1, 2, 1, -1

Offset: 1

Author

Rémy Sigrist, Aug 06 2022

Keywords

• sign
• base

Comments

See A139764 and A356400 for similar sequences.

For n > 1, the greatest term in the negaFibonacci representation of n is A280511(n-1).

Examples

			For n = 11:
- using F(-k) = A039834(k):
- 11 = F(-1) + F(-4) + F(-7),
- so a(11) = F(-1) = 1.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10946
• Wikipedia, NegaFibonacci coding
• Index entries for sequences related to Zeckendorf expansion of n

Crossrefs

Cf. A001519, A039834, A139764, A280511, A356400.

Programs

PARI

a(n) = { my (v=0, neg=0, pos=0, f); for (e=0, oo, f=fibonacci(-1-e); if (f<0, neg+=f, pos+=f); if (neg <=n && n <= pos, while (n, if (f<0, neg-=f, pos-=f); if (neg > n || n > pos, v=f; n-=f;); f=fibonacci(-1-e--);); return (v););); }

Formula

a(n) = n iff n belongs to A001519.