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A066756 Smallest number that requires n^3 steps to reach 1 in its Collatz trajectory (counting x/2 and 3x+1 steps). 0
1, 2, 6, 65, 673, 342, 2919, 129991, 1590511, 301695657, 1412987847 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=0..10.

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

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.

EXAMPLE

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.

CROSSREFS

Cf. A006577, A066773.

Sequence in context: A052522 A193609 A061999 * A070872 A055685 A262047

Adjacent sequences:  A066753 A066754 A066755 * A066757 A066758 A066759

KEYWORD

more,nonn

AUTHOR

Randall L. Rathbun, Jan 18 2002

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

STATUS

approved

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Last modified May 21 10:41 EDT 2022. Contains 353908 sequences. (Running on oeis4.)