A074474 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 4n+3.

7, 12, 9, 12, 7, 9, 97, 92, 7, 14, 9, 89, 7, 9, 12, 89, 7, 84, 9, 14, 7, 9, 74, 14, 7, 69, 9, 51, 7, 9, 14, 25, 7, 12, 9, 12, 7, 9, 66, 35, 7, 48, 9, 14, 7, 9, 12, 22, 7, 14, 9, 22, 7, 9, 14, 51, 7, 20, 9, 33, 7, 9, 45, 22, 7, 12, 9, 12, 7, 9, 40, 17, 7, 14, 9, 22, 7, 9, 12, 35, 7, 35, 9, 14

Offset: 1

Author

Labos Elemer, Sep 19 2002

Keywords

• nonn

Examples

			n=6: 4n-1=23, the list={23,70,35,106,53,160,80,40,20, 10,5,16,8,4,2,1} sinks first below iv=23 at 20, the 9th term, so a(6)=9. Observe several (provable) modular rules with respect of initial value: e.g. regular appearance of 9 and 7.
		

Crossrefs

Cf. A006370, A074472, A074473.

Programs

Mathematica

Table[Function[k, Length@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, k, # >= k &]][4 n - 1], {n, 120}] (* Michael De Vlieger, Feb 20 2017 *)

Formula

a(n)=A074473[4n-1]