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

1,7

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A006370, A006577, A070165, A078719, A286380

Sequence in context: A277080 A055240 A174559 * A273128 A183035 A115634

Adjacent sequences: A334037 A334038 A334039 * A334041 A334042 A334043

Keyword

nonn

Author

Hamid Kulosman, May 11 2020

Status

approved