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Search: id:A135730
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| A135730 |
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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. |
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5
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| 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)
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OFFSET
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1,3
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COMMENT
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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.
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PROGRAM
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(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
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CROSSREFS
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Cf. A001281, A037084, A039500-A039505, A135727-A135729. A006370, A006577 (Collatz 3x+1 problem).
Sequence in context: A016690 A136715 A077116 this_sequence A058546 A091435 A118441
Adjacent sequences: A135727 A135728 A135729 this_sequence A135731 A135732 A135733
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KEYWORD
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easy,nonn
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AUTHOR
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 26 2007
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