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

0,2

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

Equals A061984(n) + 1.

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

Sequence in context: A075084 A086593 A073757 * A355729 A049448 A354547

Adjacent sequences: A088465 A088466 A088467 * A088469 A088470 A088471

Keyword

nonn

Author

Michael Somos, Oct 02 2003

Status

approved