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%I #64 Mar 25 2013 14:56:01
%S 0,0,3,0,1,4,5,0,8,2,3,5,1,6,7,0,1,9,3,0,1,4,5,0,6,2,77,7,1,8,72,0,1,
%T 2,3,10,1,4,10,0,75,2,3,5,1,6,70,0,1,7,3,0,1,78,78,0,6,2,8,9,1,73,73,
%U 0,1,2,3,0,1,4,68,0,81,2,3,5,1,11,7,0,1,76
%N Number of halving and tripling steps to reach the largest value in the Collatz (3x+1) trajectory of n.
%C a(n) = 0 if n is a power of 2, as a(1) = a(2) = a(4) = ... = 0; however a(20) = a(24) = ... = 0 also and as such the condition (n = 2^k, k>=0) is sufficient but not necessary for a(n) = 0.
%H Alois P. Heinz, <a href="/A220421/b220421.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A087225(n) - 1.
%e a(3) = 3 because the Collatz trajectory for 3 is [3, 10, 5, 16, 8, 4, 2, 1], reaching the largest term, 16, in three steps.
%e a(4) = 0 because the Collatz trajectory only goes down from 4.
%e a(20) = 0: 20 is the largest term in [20, 10, 5, 16, 8, 4, 2, 1].
%t Collatz[n_] :=NestWhileList[If[EvenQ[#], #/2, 3*# + 1] &, n, # > 1 &]; Table[Position[Collatz[n], Max[Collatz[n]]] - 1, {n, 82}](* Jayanta Basu, Mar 24 2013 *)
%Y Cf. A006577, A014682, A025586.
%K nonn
%O 1,3
%A _Jayanta Basu_, Feb 19 2013
%E More terms from _Alois P. Heinz_, Feb 20 2013
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