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
Examples
For n = 11: - using F(-k) = A039834(k): - -11 = F(-4) + F(-6), - so a(11) = F(-4) = -3.
Links
Programs
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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););); }
Formula
a(n) = -n iff n belongs to A001906.
Comments