A182535 Number of terms in Zeckendorf representation of prime(n).

1, 1, 1, 2, 2, 1, 3, 3, 2, 2, 3, 2, 3, 3, 2, 4, 3, 3, 4, 3, 3, 3, 4, 1, 2, 4, 3, 3, 4, 3, 4, 3, 4, 4, 2, 3, 2, 4, 3, 3, 3, 3, 3, 4, 5, 2, 5, 4, 5, 5, 1, 3, 2, 3, 3, 4, 3, 4, 4, 4, 4, 3, 5, 4, 5, 4, 4, 4, 5, 5, 5, 4, 5, 6, 2, 3, 4, 4, 3, 4, 3, 4, 5, 3, 4, 4, 5, 5, 4, 5, 3, 3, 3, 5, 6, 4, 5, 2, 3, 5, 4, 4, 4, 5, 5

Offset: 1

Author

Alex Ratushnyak, May 05 2012

Keywords

• nonn

Comments

Alternately, the minimum number of Fibonacci numbers which sum to prime(n). - Alan Worley, Apr 17 2015

Examples

			prime(4)=7, and 7 is represented as 5+2, so a(4)=2.
prime(7)=17, and 17 is represented as 13+3+1, so a(7)=3.
		

Links

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

Crossrefs

Cf. A007895, A020908, A020910, A025496-A025502.

Programs

Mathematica

f[n_Integer] := Block[{k = Ceiling[ Log[ GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k--]; Count[fr, 1]]; f@# & /@ Prime@ Range@ 105 (* Robert G. Wilson v, Apr 22 2015 *)

Formula

a(n) = A007895(A000040(n)).