

A153330


Differences in adjacent elements of the sequence quantifying the steps needed for n to converge to 1 in the Collatz Conjecture.


2



1, 6, 5, 3, 3, 8, 13, 16, 13, 8, 5, 0, 8, 0, 13, 8, 8, 0, 13, 0, 8, 0, 5, 13, 13, 101, 93, 0, 0, 88, 101, 21, 13, 0, 8, 0, 0, 13, 26, 101, 101, 21, 13, 0, 0, 88, 93, 13, 0, 0, 13, 0, 101, 0, 93, 13, 13, 13, 13, 0, 88, 0, 101, 21, 0, 0, 13, 0, 0, 88, 80, 93
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OFFSET

1,2


COMMENTS

Collatz Conjecture: Starting with any positive integer n and continually halving it when even and tripling and adding 1 to it when odd, n will always converge to 1. A006577 is the number of iterations required to turn n into 1.
The sequence may be of interest because showing that all of its elements are finite is tantamount to proving the Collatz Conjecture. However there is no obvious reason to believe that demonstrating the property for this sequence would be any simpler than showing it for A006577!


LINKS

Ian Kent, Table of n, a(n) for n = 1..10000


FORMULA

a(n)=A006577(n+1)A006577(n) for n>0.


MATHEMATICA

Differences[Table[Length[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]], {n, 80}]] (* Harvey P. Dale, Oct 10 2011 *)


CROSSREFS

Sequence in context: A245632 A158038 A259281 * A225661 A225662 A225663
Adjacent sequences: A153327 A153328 A153329 * A153331 A153332 A153333


KEYWORD

easy,sign


AUTHOR

Ian Kent, Dec 23 2008


STATUS

approved



