A220421 Number of halving and tripling steps to reach the largest value in the Collatz (3x+1) trajectory of n.

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

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 * A352493 A106683 A139601

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