OFFSET
1,2
COMMENTS
a(n) > c*n*log(n)*log(log(n))*log(log(log(n)))*...*log(log...(log(n))...) (k layers) for any sufficient large n, any constant c and any positive integer k.
The sum of 1/a(i) for i = 1, 2, 3, ... diverges extremely slowly.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
KeyTo9_Fans, A Chinese post discussing the sum of 1/a(i)
Fedor Petrov, The proof of the divergence of the sum of 1/a(i), Mathoverflow, Sep 2017.
MAPLE
f:= proc(n) option remember;
procname(n-1)+procname(floor(log(n)))
end proc:
f(1):= 1: f(2):= 2:
map(f, [$1..100]); # Robert Israel, Sep 28 2017
MATHEMATICA
a[n_] := a[n] = If[n <= 2, n, a[n - 1] + a[Floor@ Log@ n]]; Array[a, 62] (* Michael De Vlieger, Sep 21 2017 *)
PROG
(PARI) a(n) = if (n<=2, n, a(n-1) + a(floor(log(n)))); \\ Michel Marcus, Sep 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Yi Yang, Sep 20 2017
STATUS
approved