A331089 Positive numbers k such that -k and -(k + 1) are both negative negaFibonacci-Niven numbers (A331088).

1, 2, 3, 15, 20, 21, 44, 50, 54, 55, 56, 57, 75, 104, 110, 111, 115, 128, 141, 152, 175, 207, 264, 291, 304, 308, 335, 351, 363, 376, 377, 380, 392, 398, 399, 435, 452, 455, 534, 584, 594, 605, 623, 654, 735, 740, 744, 753, 795, 804, 875, 884, 897, 924, 964, 968

Offset: 1

Author

Amiram Eldar, Jan 08 2020

Keywords

• nonn
• base

Comments

The Fibonacci numbers F(6*k + 2) and F(6*k + 4) are terms.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A328209, A328213, A330927, A330931, A331086, A331088.

Programs

Mathematica

ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
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];
negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
negFibQ[n_] := Divisible[n, negaFibTermsNum[-n]];
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