

A112695


Number of steps needed to reach 4,2,1 in Collatz' 3*n+1 conjecture.


8



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
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OFFSET

1,2


COMMENTS

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.


REFERENCES

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.


LINKS

Table of n, a(n) for n=1..70.
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


EXAMPLE

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.


CROSSREFS

Essentially the same sequence as A139399.
Cf. A006370, A006577.
Sequence in context: A212248 A208476 A247449 * A215078 A067881 A024714
Adjacent sequences: A112692 A112693 A112694 * A112696 A112697 A112698


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Oct 31 2005


STATUS

approved



