A331088 Positive numbers k such that -k is a negative negaFibonacci-Niven number, i.e., divisible by the number of terms in its negaFibonacci representation (A331084).

1, 2, 3, 4, 6, 8, 12, 15, 16, 18, 20, 21, 22, 24, 27, 30, 36, 42, 44, 45, 48, 50, 51, 54, 55, 56, 57, 58, 60, 66, 72, 75, 76, 80, 84, 90, 92, 96, 100, 104, 105, 108, 110, 111, 112, 115, 116, 120, 124, 126, 128, 129, 132, 136, 138, 141, 142, 144, 150, 152, 153, 156, 168, 170, 172, 175, 176, 180, 184, 186, 190, 192, 196, 198

Offset: 1

Author

Amiram Eldar, Jan 08 2020

Keywords

• nonn
• base

Comments

The k-th Fibonacci number is a term for all even k, since its negaFibonacci representation is 1 followed by (k-1) zeros.

Examples

			4 is a term since the negaFibonacci representation of -4 is 1010 whose sum of digits is 1 + 0 + 1 + 0 = 2 which is a divisor of 4.
		

Links

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

Crossrefs

Cf. A005349, A215023, A328208, A328212, A331083, A331084, A331085.

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[200], Divisible[#, negaFibTermsNum[-#]] &]