OFFSET
1,1
COMMENTS
Numbers of the form F(6*k + 1) - 1, where F(m) is the m-th Fibonacci number, are terms.
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.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
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 = 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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 08 2020
STATUS
approved