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A135730 Number of steps to reach the minimum of the final cycle under iterations of the map A001281: x->3x-1 if x odd, x/2 else. +0
5
0, 1, 4, 2, 0, 5, 3, 3, 11, 1, 6, 6, 9, 4, 9, 4, 0, 12, 7, 2, 8, 7, 3, 7, 16, 10, 5, 5, 10, 10, 6, 5, 19, 1, 13, 13, 14, 8, 13, 3, 9, 9, 8, 8, 22, 4, 16, 8, 17, 17, 11, 11, 16, 6, 12, 6, 29, 11, 11, 11, 7, 7, 19, 6, 37, 20, 20, 2, 19, 14, 19, 14, 15, 15, 9, 9, 14, 14, 14, 4 (list; graph; listen)
OFFSET

1,3

COMMENT

Under iterations of the map A001281, the orbit of any positive integer seems to end in one of 3 possible cycles, having 1, 5 resp. 17 as smallest element. This sequence gives the number of iterations needed to reach one of these values. Maybe it would be more natural to count the number of iterations needed to reach /any/ element of the final cycle.

PROGRAM

(PARI) A135730(n)=local(c=0); while( n>17 | n != 17 & n != 5 & n != 1, c++; if( n%2, n=3*n-1, n>>=1)); c

CROSSREFS

Cf. A001281, A037084, A039500-A039505, A135727-A135729. A006370, A006577 (Collatz 3x+1 problem).

Sequence in context: A016690 A136715 A077116 this_sequence A144102 A058546 A091435

Adjacent sequences: A135727 A135728 A135729 this_sequence A135731 A135732 A135733

KEYWORD

easy,nonn

AUTHOR

M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 26 2007

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Last modified December 8 08:31 EST 2009. Contains 170430 sequences.


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