login
A182535
Number of terms in Zeckendorf representation of prime(n).
13
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
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
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, May 05 2012
STATUS
approved