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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)