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A008908 Number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem. 26
1, 2, 8, 3, 6, 9, 17, 4, 20, 7, 15, 10, 10, 18, 18, 5, 13, 21, 21, 8, 8, 16, 16, 11, 24, 11, 112, 19, 19, 19, 107, 6, 27, 14, 14, 22, 22, 22, 35, 9, 110, 9, 30, 17, 17, 17, 105, 12, 25, 25, 25, 12, 12, 113, 113, 20, 33, 20, 33, 20, 20, 108, 108, 7, 28, 28, 28, 15, 15, 15, 103 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(A033496(n)) = A159999(A033496(n)). [From Reinhard Zumkeller, May 04 2009]

When Collatz 3N+1 function is seen as an isometry over the dyadics, the halving step necessarily following each tripling is not counted, hence N->N/2, if even, but N-> (3N+1)/2, if odd. Counting steps thus until reaching 1 leads to sequence A064433. [Michael Vielhaber (vielhaber(AT)gmail.com), Nov 18 2009]

a(n) = A006666(n) + A078719(n).

a(n) = length of n-th row in A070165. - Reinhard Zumkeller, May 11 2013

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E16.

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.

Wikipedia, Collatz conjecture

Dave's Integer Math Page, Integer Calculator: Compute 3x+1 [broken link?]

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

FORMULA

a(n) = A006577(n) + 1.

a(n) = f(n,1) with f(n,x) = if n=1 then x else f(A006370(n),x+1). [Reinhard Zumkeller, May 04 2009]

MATHEMATICA

Table[Length[NestWhileList[If[EvenQ[ # ], #/2, 3 # + 1] &, i, # != 1 &]], {i, 75}]

PROG

(Haskell)

a008908 = length . a070165_row

-- Reinhard Zumkeller, May 11 2013, Aug 30, Jul 19 2011

CROSSREFS

Cf. A006577, A006370, A006667, A075677.

Sequence in context: A169844 A076123 A021783 * A050077 A185576 A133840

Adjacent sequences:  A008905 A008906 A008907 * A008909 A008910 A008911

KEYWORD

nonn,nice,look

AUTHOR

N. J. A. Sloane, R. W. Gosper

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001

STATUS

approved

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Last modified December 18 02:18 EST 2014. Contains 252072 sequences.