

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
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OFFSET

0,2


COMMENTS

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


REFERENCES

R. K. Guy, Problem E16, Unsolved Problems in Number Theory, 2nd edition, SpringerVerlag, NY pp. 215218


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



