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 A006667 Number of tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached. (Formerly M0019) 48
 0, 0, 2, 0, 1, 2, 5, 0, 6, 1, 4, 2, 2, 5, 5, 0, 3, 6, 6, 1, 1, 4, 4, 2, 7, 2, 41, 5, 5, 5, 39, 0, 8, 3, 3, 6, 6, 6, 11, 1, 40, 1, 9, 4, 4, 4, 38, 2, 7, 7, 7, 2, 2, 41, 41, 5, 10, 5, 10, 5, 5, 39, 39, 0, 8, 8, 8, 3, 3, 3, 37, 6, 42, 6, 3, 6, 6, 11, 11, 1, 6, 40, 40, 1, 1, 9, 9, 4, 9, 4, 33, 4, 4, 38 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A075680, which gives the values for odd n, isolates the essential behavior of this sequence. - T. D. Noe, Jun 01 2006 a(n) = A078719(n) - 1; a(A000079(n))=0; a(A062052(n))=1; a(A062053(n))=2; a(A062054(n))=3; a(A062055(n))=4; a(A062056(n))=5; a(A062057(n))=6; a(A062058(n))=7; a(A062059(n))=8; a(A062060(n))=9. - Reinhard Zumkeller, Oct 08 2011 A033959 and A033958 give record values and where they occur. - Reinhard Zumkeller, Jan 08 2014 a(n*2^k) = a(n), for all k >= 0. - L. Edson Jeffery, Aug 11 2014 REFERENCES J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 204, Problem 22. R. K. Guy, Unsolved Problems in Number Theory, E16. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, 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. Eric Weisstein's World of Mathematics, Collatz Problem. Wikipedia, Collatz conjecture FORMULA a(1) = 0, a(n) = a(n/2) if n is even, a(n) = a(3n+1)+1 if n>1 is odd. The Collatz conjecture is that this defines a(n) for all n >= 1. a(n) = floor(log(2^A006666(n)/n)/log(3)). - Joe Slater, Aug 30 2017 MATHEMATICA Table[Count[Differences[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]], _?Positive], {n, 100}] (* Harvey P. Dale, Nov 14 2011 *) PROG (PARI) for(n=2, 100, s=n; t=0; while(s!=1, if(s%2==0, s=s/2, s=(3*s+1)/2; t++); if(s==1, print1(t, ", "); ); )) (Haskell) a006667 = length . filter odd . takeWhile (> 2) . (iterate a006370) a006667_list = map a006667 [1..] -- Reinhard Zumkeller, Oct 08 2011 (Python) def a(n):     if n==1: return 0     x=0     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 range(1, 101)] # Indranil Ghosh, Apr 14 2017 CROSSREFS Equals A078719(n)-1. Cf. A006370, A006666 (halving steps), A092893, A127789 (record indices of 2^A006666(n)/(3^a(n)*n)). Sequence in context: A127767 A292577 A055509 * A112570 A127755 A180662 Adjacent sequences:  A006664 A006665 A006666 * A006668 A006669 A006670 KEYWORD nonn,nice,hear,changed 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 STATUS approved

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Last modified December 11 07:47 EST 2019. Contains 329914 sequences. (Running on oeis4.)