

A008908


Number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem.


27



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
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OFFSET

1,2


COMMENTS

a(A033496(n)) = A159999(A033496(n)).  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 nth 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), 323.
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
(PARI) a(n)=my(c=1); while(n>1, n=if(n%2, 3*n+1, n/2); c++); c \\ Charles R Greathouse IV, May 18 2015


CROSSREFS

Cf. A006577, A006370, A006667, A075677.
Sequence in context: A169844 A076123 A021783 * A050077 A261715 A185576
Adjacent sequences: A008905 A008906 A008907 * A008909 A008910 A008911


KEYWORD

nonn,nice,look


AUTHOR

N. J. A. Sloane, Bill Gosper


EXTENSIONS

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


STATUS

approved



