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Search: id:A096010
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| A096010 |
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Number of different cycles computed with the generalized 3x+1 problem using C=2, B=Cn+m, A=C^m. |
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+0
1
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| 2, 2, 3, 3, 5, 7, 11, 17, 31, 53, 95, 173, 317, 587, 1097, 2049, 3857, 7287, 13799, 26217
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.
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FORMULA
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Generalize the 3x+1-Problem from S:= S / 2 if S is even, S:= (S * 3) + 1 if S is odd to S:= S / C if C | S S:= (S * B) + A otherwise. For B=Cn+A, A=C^m the number of different cycles z are computed. Every S leads to a cycle, so it can be conjectured that the number of cycles is infinite. But the number of different cycles seems to be finite. It is conjectured that the last new cycle occurs at the starting number S = B. This was tested with A=1; B=3; C=2 up to S=100000000.
a(n) = A000016(n)+1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 14 2006
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EXAMPLE
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a(9)=59
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CROSSREFS
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A008965 is the same sequence as this with A = -C^m.
Sequence in context: A133277 A133276 A055501 this_sequence A102330 A103403 A052473
Adjacent sequences: A096007 A096008 A096009 this_sequence A096011 A096012 A096013
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KEYWORD
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nonn
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AUTHOR
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Peter Lengler (PeterLengler(AT)t-online.de), Jul 20 2004
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