|
|
A025501
|
|
Number of terms in Zeckendorf representation of 9^n.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|