A331085 Positive negaFibonacci-Niven numbers: positive numbers divisible by the number of terms in their negaFibonacci representation (A331083).

1, 2, 4, 5, 6, 9, 10, 12, 13, 14, 18, 24, 26, 27, 30, 34, 36, 48, 55, 60, 64, 68, 69, 72, 78, 84, 86, 87, 88, 89, 90, 93, 94, 96, 99, 100, 102, 108, 110, 112, 116, 120, 140, 144, 150, 155, 156, 160, 172, 176, 177, 178, 180, 183, 184, 188, 192, 195, 196, 200, 204

Offset: 1

Author

Amiram Eldar, Jan 08 2020

Keywords

• nonn
• base

Comments

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

Examples

			4 is a term since the negaFibonacci representation of 4 is 10010 whose sum of digits is 1 + 0 + 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, A215022, A328208, A328212, A331083.

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[#]] &]