A066756 Smallest number that requires n^3 steps to reach 1 in its Collatz trajectory (counting x/2 and 3x+1 steps).

1, 2, 6, 65, 673, 342, 2919, 129991, 1590511, 301695657, 1412987847

Offset: 0

Author

Randall L Rathbun, Jan 18 2002

Keywords

• nonn
• more

Comments

a(11) > 7*10^11. - Donovan Johnson

Examples

			a(2) = 6 since the trajectory of 6 requires 2^3 = 8 steps to reach 1 (the trajectory is 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1), and 6 is the smallest number for which this is the case.
		

References

• R. K. Guy, Problem E16, Unsolved Problems in Number Theory, 2nd edition, Springer-Verlag, NY pp. 215-218

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006577, A066773.

Formula

Mapping at each step for Collatz problem: x -> x/2 if n is even, else x -> 3*x+1; count the steps until x=1.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2002

a(10) from Donovan Johnson, Nov 13 2010

Edited by Jon E. Schoenfield, Jan 28 2014