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

Author

Gary W. Adamson, Feb 08 2007

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A006577, A061641.

Formula

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

Extensions

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

Name edited by Michel Marcus, Feb 28 2020