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Search: id:A037084
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| A037084 |
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Positive integers not going to 1 under iterations of the map in A001281: n->3n-1 if n odd, n->n/2 if n even. |
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+0
12
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| 5, 7, 9, 10, 13, 14, 17, 18, 19, 20, 21, 23, 25, 26, 27, 28, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 61, 62, 63, 66, 67, 68, 70, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 89, 90, 91, 92, 93, 94, 98, 99, 100, 102
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Up to at least 100000000, every number reaches 1, 5 or 17.
Conjecture : for any x, the iterated process "x ->3x-1" if x is odd or "x ->x/2" if x is even leads to one of the following three cycles: (1, 2), (5, 14, 7, 20, 10), (41, 122, 61, 182, 91, 272, 136, 68, 34, 17, 50, 25, 74, 37, 110, 55, 164, 82). - Benoit Cloitre (benoit7848c(AT)orange.fr), May 14 2002
Complement (in N*) of A039500 ; union of A039501 and A039502 (conjectured). - M. F. Hasler, Nov 26 2007
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EXAMPLE
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Iterations of f starting at 3 are 3,8,4,2,1 - thus 3 is not in the sequence. Iterations starting at 5 are 5,14,7,20,10,5 -periodic and 1 is not among these values, so 5 is in the sequence.
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PROGRAM
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(PARI) A037084( end=999, n=0 /*starting value -1 */)={ for( i=n, end, n=i; while( n > 17 | n > 5 & n < 17, if( n%2, n=3*n-1, n>>=1)); if( n > 4, print1(i", ")))} \\ - M. F. Hasler, Nov 26 2007
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CROSSREFS
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Cf. A001281, A039500-A039505.
Cf. A006370, A006577 (Collatz problem: 3n+1).
Sequence in context: A153031 A138892 A005523 this_sequence A018935 A039501 A114255
Adjacent sequences: A037081 A037082 A037083 this_sequence A037085 A037086 A037087
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KEYWORD
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nonn,easy
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AUTHOR
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Robert W. Craigen (craigen(AT)fresno.edu)
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net), Feb 15 1999.
Edited by M. F. Hasler (maximilian.hasler(AT)gmail.com), Nov 26 2007.
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