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A331087 Starts of runs of 3 consecutive positive negaFibonacci-Niven numbers (A331085).

%I A331087 #10 Jan 09 2020 03:06:32
%S A331087 4,12,86,87,88,176,230,231,232,320,464,655,1194,1592,1596,1854,1914,
%T A331087 2815,3016,3294,4124,4178,4179,4180,4268,4412,5663,5755,8360,9894,
%U A331087 10614,10703,10915,10975,13936,14994,15114,15714,17630,18976,19984,20824,21835,23175,23513
%N A331087 Starts of runs of 3 consecutive positive negaFibonacci-Niven numbers (A331085).
%C A331087 Numbers of the form F(6*k + 1) - 1, where F(m) is the m-th Fibonacci number, are terms.
%C A331087 Numbers of the form F(k) - 3, where k is congruent to {5, 11, 13, 19} mod 24 (A269819) are starts of runs of 5 consecutive negaFibonacci-Niven numbers.
%H A331087 Amiram Eldar, <a href="/A331087/b331087.txt">Table of n, a(n) for n = 1..10000</a>
%t A331087 ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
%t A331087 f[1] = 1; f[n_] := If[n > 0, i = ind[n - 1]; If[EvenQ[i], i++]; i, i = ind[-n]; If[OddQ[i], i++]; i];
%t A331087 negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
%t A331087 negFibQ[n_] := Divisible[n, negaFibTermsNum[n]];
%t A331087 nConsec = 3; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec + 1; While[c < 55, If[And @@ neg, c++; AppendTo[seq, k - nConsec]];neg = Join[Rest[neg], {negFibQ[k]}]; k++]; seq
%Y A331087 Cf. A000045, A154701, A269819, A328210, A328214, A330932, A331085.
%K A331087 nonn,base
%O A331087 1,1
%A A331087 _Amiram Eldar_, Jan 08 2020