A292620 a(n) = a(n-1) + a(floor(log_2(n))), with a(1) = 1.

1, 2, 3, 5, 7, 9, 11, 14, 17, 20, 23, 26, 29, 32, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 122, 129, 136, 143, 150, 157, 164, 171, 178, 185, 192, 199, 206, 213, 220, 227, 234, 241, 248, 255, 262, 269, 276, 283, 290, 297, 304, 311

Offset: 1

Author

Yi Yang, Sep 20 2017

Keywords

• nonn
• easy

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)

Crossrefs

Cf. A000523, A292621.

Programs

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 *)

PARI

a(n) = if (n<=2, n, a(n-1) + a(logint(n, 2))); \\ Michel Marcus, Sep 21 2017