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