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A356400
a(n) is the smallest term (in absolute value) in the negaFibonacci representation of -n.
2
-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.
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
KEYWORD
sign,base
AUTHOR
Rémy Sigrist, Aug 06 2022
STATUS
approved