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

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%I A356400 #7 Aug 07 2022 15:37:09
%S A356400 -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,
%T A356400 -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,
%U A356400 1,-3,-1,1,2,1,-8,-1,1,-3,-1,1,2,1,5,-1,1,2,1
%N A356400 a(n) is the smallest term (in absolute value) in the negaFibonacci representation of -n.
%C A356400 See A139764 and A356399 for similar sequences.
%H A356400 Rémy Sigrist, <a href="/A356400/b356400.txt">Table of n, a(n) for n = 1..10946</a>
%H A356400 Wikipedia, <a href="https://en.wikipedia.org/wiki/NegaFibonacci_coding">NegaFibonacci coding</a>
%H A356400 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F A356400 a(n) = -n iff n belongs to A001906.
%e A356400 For n = 11:
%e A356400 - using F(-k) = A039834(k):
%e A356400 - -11 = F(-4) + F(-6),
%e A356400 - so a(11) = F(-4) = -3.
%o A356400 (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););); }
%Y A356400 Cf. A001906, A039834, A139764, A356399.
%K A356400 sign,base
%O A356400 1,3
%A A356400 _Rémy Sigrist_, Aug 06 2022