A334040 Number of odd numbers larger than n in the Collatz trajectory of n.

0, 0, 1, 0, 0, 0, 3, 0, 3, 0, 2, 0, 0, 1, 3, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 38, 0, 0, 2, 36, 0, 0, 0, 1, 0, 0, 0, 4, 0, 35, 0, 2, 0, 0, 1, 34, 0, 0, 0, 1, 0, 0, 33, 35, 0, 1, 0, 3, 0, 0, 32, 33, 0, 0, 0, 1, 0, 0, 0, 31, 0, 33, 0, 2, 0, 0, 2, 4, 0, 0, 31, 32

Offset: 1

Author

Hamid Kulosman, May 11 2020

Keywords

• nonn

Examples

			For n=7 the Collatz process is: 7,22,(11),34,(17),52,26,(13),40,20,10,5,16,8,4,2,1. The numbers in the parentheses are odd numbers in the Collatz process for n=7 that are bigger than 7. There are three of them, hence a(7)=3.
		

Links

• Markus Sigg, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale).
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A006577, A070165, A078719, A286380

Programs

Mathematica

Table[Count[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&],?(#>n&&OddQ[#]&)],{n,90}] (* _Harvey P. Dale, Aug 03 2023 *)

PARI

f(n) = if (n%2, 3*n+1, n/2);
a(n) = {my(nb = 0, m=n); while ((n=f(n)) != 1, if ((n % 2) && (n>m), nb++)); nb;} \\ Michel Marcus, Jun 01 2020