A224166 Number of halving and tripling steps to reach the last number of the cycle in the Collatz (3x+1) problem for the negative integers (the initial term is counted).

2, 2, 5, 3, 5, 6, 5, 4, 12, 5, 7, 7, 10, 5, 10, 5, 18, 13, 8, 5, 24, 8, 19, 8, 18, 11, 8, 6, 11, 11, 22, 6, 29, 18, 14, 14, 18, 9, 14, 6, 18, 25, 9, 9, 23, 20, 17, 9, 27, 18, 12, 12, 17, 9, 18, 7, 30, 12, 12, 12, 18, 23, 20, 7, 38, 30, 21, 18, 20, 15, 20, 15

Offset

1,1

Links

Table of n, a(n) for n=1..72.

Formula

a(n) = A224183(n) + 1.

Example

a(10) = 5 because the trajectory of -10 is -10 -> -5 -> -14 -> -7 -> -20 -> -10 and -10 is the last term of the cycle, hence 5 iterations where the first term -10 is counted.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, UnsameQ, All]; Table[s = Collatz[-n]; len = Length[s] - 2; If[s[[-1]] == 2, len = len - 1]; len+1, {n, 1, 100}]

Crossrefs

Cf. A006577, A224183.

Sequence in context: A130327 A224361 A341443 * A286109 A239665 A178179

Adjacent sequences: A224163 A224164 A224165 * A224167 A224168 A224169

Keyword

nonn

Author

Michel Lagneau, Apr 01 2013

Extensions

a(1) changed to 2 by Pontus von Brömssen, Jan 24 2021

Status

approved