

A220421


Number of halving and tripling steps to reach the largest value in the Collatz (3x+1) trajectory of n.


3



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, 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, 0, 1, 2, 3, 0, 1, 4, 68, 0, 81, 2, 3, 5, 1, 11, 7, 0, 1, 76
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OFFSET

1,3


COMMENTS

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.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A087225(n)  1.


EXAMPLE

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.
a(4) = 0 because the Collatz trajectory only goes down from 4.
a(20) = 0: 20 is the largest term in [20, 10, 5, 16, 8, 4, 2, 1].


MATHEMATICA

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 *)


CROSSREFS

Cf. A006577, A014682, A025586.
Sequence in context: A143949 A124323 A250104 * A106683 A139601 A213191
Adjacent sequences: A220418 A220419 A220420 * A220422 A220423 A220424


KEYWORD

nonn


AUTHOR

Jayanta Basu, Feb 19 2013


EXTENSIONS

More terms from Alois P. Heinz, Feb 20 2013


STATUS

approved



