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

1,2

Comments

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

Links

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

Example

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.

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[#]] &]

Crossrefs

Cf. A005349, A215022, A328208, A328212, A331083.

Sequence in context: A254820 A332570 A047435 * A132791 A352320 A352508

Adjacent sequences: A331082 A331083 A331084 * A331086 A331087 A331088

Keyword

nonn,base

Author

Amiram Eldar, Jan 08 2020

Status

approved