OFFSET
1,2
COMMENTS
a(n) > c*n*log_2(n)*log_2(log_2(n))*log_2(log_2(log_2(n)))*...*log_2(log_2...(log_2(n))...) (k layers) for any sufficiently large n, any constant c and any positive integer k.
The sum of 1/a(i) for i = 1, 2, 3, ... converges extremely slowly to the limit 5.70....
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
KeyTo9_Fans, A Chinese post discussing the sum of 1/a(i)
MAPLE
f:= proc(n) option remember; procname(n-1)+procname(ilog2(n)) end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Sep 24 2017
MATHEMATICA
a[n_] := a[n] = If[n == 1, 1, a[n - 1] + a[Floor@ Log2@ n]]; Array[a, 59] (* Michael De Vlieger, Sep 21 2017 *)
PROG
(PARI) a(n) = if (n<=2, n, a(n-1) + a(logint(n, 2))); \\ Michel Marcus, Sep 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Yi Yang, Sep 20 2017
STATUS
approved