|
%I #22 Sep 08 2022 08:44:53
%S 1,3,5,7,9,12,13,16,18,21,22,25,27,29,32,35,36,39,40,43,46,48,49,53,
%T 55,58,60,62,63,67,68,71,73,76,78,81,82,84,87,91,92,96,97,99,102,104,
%U 105,109,110,113,115,118,119,122,125,128,130,132,133,137,138,140,143,146
%N [ n/F_2 ] + [ n/F_3 ] + [ n/F_4 ] +..., F_n=Fibonacci numbers.
%H Vaclav Kotesovec, <a href="/A038663/a038663.jpg">Plot of a(n)/n for n = 1..100000</a>
%F G.f.: (1/(1 - x)) * Sum_{k>=2} x^Fibonacci(k)/(1 - x^Fibonacci(k)). - _Ilya Gutkovskiy_, Jul 16 2019
%F Conjecture: a(n) ~ c * n, where c = A079586 - 1. - _Vaclav Kotesovec_, Aug 30 2021
%e a(15)=[ 15/1 ]+[ 15/2 ]+[ 15/3 ]+[ 15/5 ]+[ 15/8 ]+[ 15/13 ]+[ 15/21 ]+...=32.
%p with(combinat): for n from 1 to 200 do printf(`%d,`,sum(floor(n/fibonacci(k)), k=2..15)) od:
%t Table[Sum[Floor[n/Fibonacci[k] ],{k,2,200}],{n,70}] (* _Harvey P. Dale_, Jul 21 2021 *)
%t Table[Sum[Floor[n/Fibonacci[k]], {k, 2, Log[Sqrt[5]*n]/Log[GoldenRatio] + 1}], {n, 1, 100}] (* _Vaclav Kotesovec_, Aug 30 2021 *)
%o (Magma) [&+[Floor(n/Fibonacci(k+2)):k in [0..n]]:n in [1..64]]; // _Marius A. Burtea_, Jul 16 2019
%Y Cf. A005086.
%K nonn,easy
%O 1,2
%A Antreas P. Hatzipolakis (xpolakis(AT)hol.gr)
%E More terms from _Simon Plouffe_, who points out that the first differences give A005086
%E More terms from _James A. Sellers_, Feb 19 2001
|
