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A331090 Positive numbers k such that -k, -(k + 1), and -(k + 2) are 3 consecutive negative negaFibonacci-Niven numbers (A331088).

%I A331090 #9 Jan 09 2020 03:06:47
%S A331090 1,2,20,54,55,56,110,376,398,974,986,1084,1744,2464,2524,3304,3870,
%T A331090 5223,5718,6095,6124,6184,6663,6764,6844,7142,7684,9035,9124,10590,
%U A331090 11598,11975,12606,13444,13504,14284,14915,17164,17643,17710,17714,17824,17884,18698,18905,19494,23191,24243,24785,25542,26382,27390,29644,34278,35464
%N A331090 Positive numbers k such that -k, -(k + 1), and -(k + 2) are 3 consecutive negative negaFibonacci-Niven numbers (A331088).
%C A331090 Numbers of the form F(6*k + 2) - 1 and F(6*k + 4) - 1, where F(m) is the m-th Fibonacci number, are terms.
%C A331090 If m is of the form F(k) - 1, where k > 2 is congruent to {2, 10} mod 24, then {-m, -(m + 1), -(m + 2), -(m + 3), -(m + 4)} are 5 consecutive negative negaFibonacci-Niven numbers.
%H A331090 Amiram Eldar, <a href="/A331090/b331090.txt">Table of n, a(n) for n = 1..10000</a>
%t A331090 ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
%t A331090 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 A331090 negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
%t A331090 negFibQ[n_] := Divisible[n, negaFibTermsNum[-n]];
%t A331090 nConsec = 3; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0;
%t A331090 k = nConsec+1; While[c < 55, If[And @@ neg, c++; AppendTo[seq, k - nConsec]];neg = Join[Rest[neg], {negFibQ[k]}]; k++]; seq
%Y A331090 Cf. A000045, A154701, A269819, A328210, A328214, A330932, A331087, A331088.
%K A331090 nonn,base
%O A331090 1,2
%A A331090 _Amiram Eldar_, Jan 08 2020