A025501 Number of terms in Zeckendorf representation of 9^n.

1, 2, 3, 5, 6, 7, 8, 11, 12, 12, 13, 18, 16, 15, 19, 18, 20, 20, 23, 21, 23, 28, 28, 33, 25, 33, 37, 38, 35, 31, 41, 46, 38, 50, 45, 49, 49, 44, 45, 52, 50, 52, 58, 58, 53, 54, 54, 55, 67, 57, 65, 67, 66, 74, 77, 80, 76, 79, 76, 72, 74, 83, 79, 77, 88, 83, 78, 87, 76, 88, 87, 94, 97

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..1000

Formula

a(n) = A007895(A001019(n)). - Michel Marcus, May 09 2019

Example

9^2 = 81 = F(10) + F(8) + F(5) = 55 + 21 + 5. Hence a(2) = 3.
9^3 = 729 = F(15) + F(11) + F(8) + F(6) + F(1) = 610 + 89 + 21 + 8 + 1. Hence a(3) = 5.

Mathematica

Table[Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5] * # + 3/2]/Log[GoldenRatio]]] &, 9^n, # > 1 &], 0]], {n, 0, 80}] (* Alonso del Arte, May 09 2019 *)

Crossrefs

Cf. A001019, A007895.

Sequence in context: A229993 A323252 A219255 * A028758 A028803 A050942

Adjacent sequences: A025498 A025499 A025500 * A025502 A025503 A025504

Keyword

nonn

Author

Clark Kimberling

Status

approved