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Search: id:A158379
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| A158379 |
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Period-lengths of the base-3 MR-expansions of the reciprocals of the positive integers. |
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1
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| 2, 1, 2, 2, 4, 1, 6, 1, 2, 4, 4, 2, 2, 6, 4, 3, 16, 1, 18, 2, 6, 3, 8, 1, 20, 1, 2, 6, 28, 4, 30, 7, 4, 16, 10, 2, 18, 18, 2, 2, 8, 6, 42, 8, 4, 11, 18, 3, 42, 20, 16, 4, 52, 1, 20, 3, 18, 28, 26, 2, 10, 30, 6, 15, 10, 3, 22, 12, 8, 8, 28, 1, 12, 18, 20, 18, 28, 1, 78, 1, 2, 8, 38, 6, 14, 42, 28
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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See A136042 for the definition of the MR-expansion.
It appears that if p is a prime with 3 as a primitive root (A001122), then the MR-expansion of 1/p is periodic with period p-1.
The period lengths of the base-2 MR-expansions of the reciprocals of the positive integers are given in A136043.
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EXAMPLE
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The base-3 MR-expansion of 1/5 is {2,1,0,1,2,1,0,1,...} because 1/5->3/5->9/5->4/5->12/5->7/5->2/5->6/5->1/5->..., indicating that MR(1/5,3) begins {2,1,0,1,...} and has period 4. Thus a(5)=4.
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CROSSREFS
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A001122, A007733, A115591, A136042, A136043, A136044, A155072.
Sequence in context: A049823 A143775 A003165 this_sequence A122838 A050378 A161833
Adjacent sequences: A158376 A158377 A158378 this_sequence A158380 A158381 A158382
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Mar 17 2009
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