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A331086 Positive numbers k such that k and k + 1 are both negaFibonacci-Niven numbers (A331085).

%I A331086 #11 Jan 09 2020 03:06:28
%S A331086 1,4,5,9,12,13,26,68,86,87,88,89,93,99,155,176,177,183,195,212,230,
%T A331086 231,232,233,237,243,255,320,321,327,384,395,411,415,424,464,465,471,
%U A331086 475,484,515,544,575,591,602,644,655,656,744,824,875,894,924,1043,1115,1127
%N A331086 Positive numbers k such that k and k + 1 are both negaFibonacci-Niven numbers (A331085).
%C A331086 Fibonacci numbers F(6*k - 1) and F(6*k) are terms.
%H A331086 Amiram Eldar, <a href="/A331086/b331086.txt">Table of n, a(n) for n = 1..10000</a>
%t A331086 ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
%t A331086 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 A331086 negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
%t A331086 negFibQ[n_] := Divisible[n, negaFibTermsNum[n]];
%t A331086 nConsec = 2; 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 A331086 Cf. A328209, A328213, A330927, A330931, A331085.
%K A331086 nonn,base
%O A331086 1,2
%A A331086 _Amiram Eldar_, Jan 08 2020