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A292620 a(n) = a(n-1) + a(floor(log_2(n))), with a(1) = 1. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000523, A292621.

Sequence in context: A102422 A062427 A127721 * A241907 A065130 A023535

Adjacent sequences:  A292617 A292618 A292619 * A292621 A292622 A292623

KEYWORD

nonn,easy

AUTHOR

Yi Yang, Sep 20 2017

STATUS

approved

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Last modified November 13 21:28 EST 2019. Contains 329106 sequences. (Running on oeis4.)