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The product of the numbers in the Collatz trajectory of a(n) is the n-th largest such product.
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%I #6 Mar 30 2012 17:22:56

%S 1,2,4,8,16,5,32,10,3,6,20,64,12,40,21,24,128,13,42,80,48,26,256,84,

%T 160,52,96,85,17,168,53,512,104,320,192,34,170,106,11,336,208,68,1024,

%U 384,22,35,640,340,212,7,69,136,44,672,416,70,14,341,213,113,768,2048,1280

%N The product of the numbers in the Collatz trajectory of a(n) is the n-th largest such product.

%C That is, a(n) is the number k such that A178168(k) = A178169(n).

%C The sequence is easy to compute by generating the Collatz tree while keeping track of the products at the leaves of the tree. At each step, extend the tree at the leaf having the smallest product.

%H T. D. Noe, <a href="/A178170/b178170.txt">Table of n, a(n) for n=1..1000</a>

%K nonn

%O 1,2

%A _T. D. Noe_, May 21 2010