A088468 a(0) = 1, a(n) = a(floor(n/2)) + a(floor(n/3)) for n > 0.

1, 2, 3, 4, 5, 5, 7, 7, 8, 9, 9, 9, 12, 12, 12, 12, 13, 13, 16, 16, 16, 16, 16, 16, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 33, 33, 33, 33, 33, 33, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 38, 38, 38, 38, 38, 38, 38, 38, 48

Offset: 0

Author

Michael Somos, Oct 02 2003

Keywords

• nonn

Comments

Record values greater than 1 occur at 3-smooth numbers: A160519(n)=a(A003586(n)) and A160519(m)A003586(n). - Reinhard Zumkeller, May 16 2009

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• A. R. Lebeck, CPS 104: Homework #3.
• Michael Penn, Erdős but simpler, Youtube video.

Crossrefs

Equals A061984(n) + 1.

Cf. A007731, A083662, A165704, A165706. - Reinhard Zumkeller, Sep 26 2009

Programs

Mathematica

a[0]=1;a[n_]:=a[n]=a[Floor[n/2]]+a[Floor[n/3]];Array[a,75,0] (* Harvey P. Dale, Aug 23 2020 *)

PARI

a(n)=if(n<1,n==0,a(n\2)+a(n\3))

Formula

Limit_{n->oo} a(n)/n = 0, as proved in Michael Penn's Youtube video (see Links). Michael Penn states in the video that this is a simplification of a problem of Paul Erdős, where the original problem is to show that limit_{n->oo} b(n)/n = 12/log(432) for b(0) = 1, b(n) = b(floor(n/2)) + b(floor(n/3)) + b(floor(n/6)) for n > 0 ({b(n)} is the sequence A007731). - Jianing Song, Sep 27 2023