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 A008908 (1 + number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem), or -1 if 1 is never reached. 31
 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 The number of steps (iterations of the map A006370) to reach 1 is given by A006577, this sequence counts 1 more. - M. F. Hasler, Nov 05 2017 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 iterations of this map until reaching 1 leads to sequence A064433. [Michael Vielhaber (vielhaber(AT)gmail.com), Nov 18 2009] 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. Nitrxgen, Collatz Calculator Wikipedia, Collatz conjecture 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). a(A033496(n)) = A159999(A033496(n)). - Reinhard Zumkeller, May 04 2009 a(n) = A006666(n) + A078719(n). a(n) = length of n-th row in A070165. - Reinhard Zumkeller, May 11 2013 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 (Python) def a(n):     if n==1: return 1     x=1     while True:         if n%2==0: n/=2         else: n = 3*n + 1         x+=1         if n<2: break     return x print [a(n) for n in xrange(1, 101)] # Indranil Ghosh, Apr 15 2017 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 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001 "Escape clause" added to definition by N. J. A. Sloane, Jun 06 2017 Edited by M. F. Hasler, Nov 05 2017 STATUS approved

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Last modified March 23 06:55 EDT 2018. Contains 301100 sequences. (Running on oeis4.)