A097051 a(n) = floor(n/a(floor(n/2))); a(1) = 1.

1, 2, 3, 2, 2, 2, 2, 4, 4, 5, 5, 6, 6, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 1

Author

Reinhard Zumkeller and Robert G. Wilson v, Jul 21 2004

Keywords

• nonn

Examples

			a(50)=floor(50/a(25))
..... a(25)=floor(25/a(12))
........... a(12)=floor(12/a(6))
................. a(6)=floor(6/a(3))
...................... a(3)=floor(3/a(1))
........................... a(1)=1
...................... a(3)=floor(3/a(1))=floor(3/1)=3
................. a(6)=floor(6/a(3))=floor(6/3)=2
........... a(12)=floor(12/a(6))=floor(12/2)=6
..... a(25)=floor(25/a(12))=floor(25/6)=4
a(50)=floor(50/a(25))=floor(50/4)=12.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A096036, A097053.

Programs

Maple

f:= proc(n) option remember;  floor(n/procname(floor(n/2))) end proc:
f(1):= 1:
map(f, [$1..200]); # Robert Israel, Jan 06 2021

Mathematica

a[1] = 1; a[n_] := a[n] = Floor[n/a[Floor[n/2]]]; Table[ a[n], {n, 94}]

Formula

If floor(log_2(n))=2k+1, then a(n) = floor(n/2^k). If floor(log_2(n))=2k, then a(n) = 2^k.

Extensions

Formula added by Max Alekseyev, Mar 02 2011