A331092 Positive numbers k such that k and k + 1 are both positive negaFibonacci-Niven numbers (A331085) and -k and -(k + 1) are both negative negaFibonacci-Niven numbers (A331088).

1, 744, 875, 924, 1115, 1575, 1704, 1955, 2904, 3815, 5495, 5844, 6125, 6335, 6824, 7136, 7314, 8154, 8225, 8360, 8784, 9414, 10535, 10744, 10935, 11976, 12047, 13194, 13404, 13475, 18024, 19368, 19943, 20615, 21791, 22224, 22560, 23807, 24143, 24576, 25752, 26424, 26999

Offset

1,2

Comments

Positive numbers k such that both k and k + 1 are in A331091.

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]] && Divisible[n, negaFibTermsNum[-n]];
nConsec = 2; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec + 1; While[c < 45, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negFibQ[k]}]; k++]; seq

Crossrefs

Intersection of A331086 and A331089.

Cf. A331085, A331088, A331091.

Sequence in context: A289141 A345547 A345800 * A235294 A331674 A235252

Adjacent sequences: A331089 A331090 A331091 * A331093 A331094 A331095

Keyword

nonn,base

Author

Amiram Eldar, Jan 08 2020

Status

approved