OFFSET
0,2
COMMENTS
Record values greater than 1 occur at 3-smooth numbers: A160519(n)=a(A003586(n)) and A160519(m)<a(m) for 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.
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
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 *)
PROG
(PARI) a(n)=if(n<1, n==0, a(n\2)+a(n\3))
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Oct 02 2003
STATUS
approved