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Search: id:A112695
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| A112695 |
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Number of steps needed to reach 4,2,1 in Collatz' 3*n+1 conjecture. |
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+0
4
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| 1, 2, 5, 0, 3, 6, 14, 1, 17, 4, 12, 7, 7, 15, 15, 2, 10, 18, 18, 5, 5, 13, 13, 8, 21, 8, 109, 16, 16, 16, 104, 3, 24, 11, 11, 19, 19, 19, 32, 6, 107, 6, 27, 14, 14, 14, 102, 9, 22, 22, 22, 9, 9, 110, 110, 17, 30, 17, 30, 17, 17, 105, 105, 4, 25, 25, 25, 12, 12, 12
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = number of iterations of the Collatz 3*x+1 map applied to n until the conjectured 4,2,1 sequence is reached.
a(n)=A006577(n)-2, n>=3, a(1)=1, a(2)=2.
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REFERENCES
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C. A. Pickover, Dr. Googols wundersame Welt der Zahlen, Deutscher Taschenbuch Verlag, Kap.14, pp. 87,193. German translation of: Wonders of numbers - Adventures in Mathematics, Mind, and Meaning, Oxford University Press 2003.
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LINKS
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Ken Conrow Collatz 3n+1 Problem.
Eric Weisstein's World of Mathematics, Collatz Problem
Index entries for sequences related to 3x+1 (or Collatz) problem
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EXAMPLE
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a(1)=1 because the sequence for n=1 is 1,4,2,1. a(4)=0 from 4,2,1.
a(7)=14 from 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.
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CROSSREFS
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Essentially the same sequence as A139399.
Cf. A006370, A006577.
Adjacent sequences: A112692 A112693 A112694 this_sequence A112696 A112697 A112698
Sequence in context: A006891 A054675 A136209 this_sequence A067881 A024714 A123342
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 31 2005
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