A127933 Number of halving and tripling steps to reach 1 from the n-th pure hailstone number in the '3x+1' problem.

0, 0, 7, 8, 16, 19, 9, 17, 20, 20, 7, 10, 23, 111, 18, 26, 21, 21, 34, 8, 29, 16, 11, 24, 112, 112, 32, 19, 107, 27, 14, 22, 115, 14, 35, 35, 22, 9, 30, 17, 17, 12, 118, 25, 25, 38, 113, 113, 69, 33, 33, 20, 20, 46, 108, 46, 121, 28, 28, 41, 15, 15, 23, 116, 116

Offset

1,3

Comments

Previous name was: A006577(k), k = pure hailstone numbers from A061641.

Impure hailstone numbers are those which occur in the trajectories of smaller numbers. Thus 5 is impure since it occurs in the trajectory of 3.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Douglas J. Shaw, The Pure Numbers Generated by the Collatz Sequence, The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, p. 194.

Formula

a(n) = A006577(A061641(n)).

Example

3 is the 3rd term of A061641, the trajectory of 3 has 7 terms: (10, 5, 16, 8, 4, 2, 1), so a(3) = 7.

Crossrefs

Cf. A006577, A061641.

Sequence in context: A125195 A099534 A318613 * A006878 A022312 A351087

Adjacent sequences: A127930 A127931 A127932 * A127934 A127935 A127936

Keyword

nonn

Author

Gary W. Adamson, Feb 08 2007

Extensions

Offset corrected and more terms added by Amiram Eldar, Feb 28 2020

Name edited by Michel Marcus, Feb 28 2020

Status

approved