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Search: id:A006667
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| A006667 |
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Number of tripling steps to reach 1 in `3x+1' problem.
(Formerly M0019)
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+0
8
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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A075680, which gives the values for odd n, isolates the essential behavior of this sequence. - T. D. Noe (noe(AT)sspectra.com), Jun 01 2006
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REFERENCES
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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.
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LINKS
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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, Link to a section of The World of Mathematics.
Index entries for sequences related to 3x+1 (or Collatz) problem
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FORMULA
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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.
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PROGRAM
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(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, ", "); ); ))
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CROSSREFS
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Equals A078719(n)-1.
Sequence in context: A025247 A127767 A055509 this_sequence A112570 A127755 A014511
Adjacent sequences: A006664 A006665 A006666 this_sequence A006668 A006669 A006670
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KEYWORD
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nonn,nice
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AUTHOR
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njas, R. W. Gosper
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001
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