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a(0) = 1, a(n) = a(floor(n/2)) + a(floor(n/3)) for n > 0.
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%I #20 Sep 27 2023 10:06:51

%S 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,

%T 21,21,21,21,21,22,22,22,22,28,28,28,28,28,28,28,28,28,28,28,28,33,33,

%U 33,33,33,33,37,37,37,37,37,37,37,37,37,37,38,38,38,38,38,38,38,38,48

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

%C 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

%H Reinhard Zumkeller, <a href="/A088468/b088468.txt">Table of n, a(n) for n = 0..10000</a>

%H A. R. Lebeck, <a href="http://www.cs.duke.edu/courses/spring03/cps104/homework/hw3.html">CPS 104: Homework #3</a>.

%H Michael Penn, <a href="https://www.youtube.com/watch?v=u7ATQEA4Hbw">Erdős but simpler</a>, Youtube video.

%F 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

%t 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 *)

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

%Y Equals A061984(n) + 1.

%Y Cf. A007731, A083662, A165704, A165706. - _Reinhard Zumkeller_, Sep 26 2009

%K nonn

%O 0,2

%A _Michael Somos_, Oct 02 2003