A331091 Positive negaFibonacci-Niven numbers k (A331085) such that -k is a negative negaFibonacci-Niven number (A331088).

1, 2, 4, 6, 12, 18, 24, 27, 30, 36, 48, 55, 60, 72, 84, 90, 96, 100, 108, 110, 112, 116, 120, 144, 150, 156, 172, 176, 180, 184, 192, 196, 208, 228, 234, 240, 246, 252, 260, 264, 288, 300, 305, 320, 328, 330, 336, 340, 360, 372, 378, 384, 396, 400, 415, 420, 460, 468, 475, 480, 492

Offset: 1

Author

Amiram Eldar, Jan 08 2020

Keywords

• nonn
• base

Comments

Positive numbers k that are divisible by the number of terms in the negaFibonacci representations of both k and -k (A215022 and A215023, respectively).

Links

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

Crossrefs

Intersection of A331085 and A331088.

Cf. A215022, A215023, A330711.

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];
Select[Range[500], Divisible[#, negaFibTermsNum[#]] && Divisible[#, negaFibTermsNum[-#]] &]