A356400 a(n) is the smallest term (in absolute value) in the negaFibonacci representation of -n.

-1, 1, -3, -1, 1, 2, 1, -8, -1, 1, -3, -1, 1, 2, 1, 5, -1, 1, 2, 1, -21, -1, 1, -3, -1, 1, 2, 1, -8, -1, 1, -3, -1, 1, 2, 1, 5, -1, 1, 2, 1, 13, -1, 1, -3, -1, 1, 2, 1, 5, -1, 1, 2, 1, -55, -1, 1, -3, -1, 1, 2, 1, -8, -1, 1, -3, -1, 1, 2, 1, 5, -1, 1, 2, 1

Offset

1,3

Comments

See A139764 and A356399 for similar sequences.

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

Formula

a(n) = -n iff n belongs to A001906.

Example

For n = 11:
- using F(-k) = A039834(k):
- -11 = F(-4) + F(-6),
- so a(11) = F(-4) = -3.

Prog

(PARI) a(n) = { my (v=0, neg=0, pos=0, f); n=-n; 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); ); ); }

Crossrefs

Cf. A001906, A039834, A139764, A356399.

Sequence in context: A095276 A246457 A089338 * A153066 A126209 A176346

Adjacent sequences: A356397 A356398 A356399 * A356401 A356402 A356403

Keyword

sign,base

Author

Rémy Sigrist, Aug 06 2022

Status

approved