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

1,4

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A126268 A193739 A345032 * A181186 A364197 A097291

Adjacent sequences: A182532 A182533 A182534 * A182536 A182537 A182538

Keyword

nonn

Author

Alex Ratushnyak, May 05 2012

Status

approved