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Search: id:A136042
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| A136042 |
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Base-2 MR-expansion of 1/29. |
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+0
7
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| 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1
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OFFSET
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1,1
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COMMENT
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The base-m MR-expansion of a positive real number x, denoted by MR(x,m), is the integer sequence {s(1),s(2),s(3),...}, where s(i) is the smallest exponent d such that (m^d)x(i)>1 and where x(i+1)=(2^d)x(i)-1, with the initialization x(1)=x. The base-2 MR-expansion of 1/29 is periodic with period length 14. Further computational results (see A136043) suggest that if p is a prime with 2 as a primitive root, then the base-2 MR-expansion of 1/p is periodic with period (p-1)/2. This has been confirmed for primes up to 2000. The base-2 MR-expansion of e-2.71828... is given in A136044.
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FORMULA
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a(n)=(1/182)*{-48*(n mod 14)+17*[(n+1) mod 14]+17*[(n+2) mod 14]-22*[(n+3) mod 14]+4*[(n+4) mod 14]+17*[(n+5) mod 14]-9*[(n+6) mod 14]+4*[(n+7) mod 14]+4*[(n+8) mod 14]+30*[(n+9) mod 14]-9*[(n+10) mod 14]-9*[(n+11) mod 14]+43*[(n+12) mod 14]+17*[(n+13) mod 14]} - Paolo P. Lava (ppl(AT)spl.at), Jan 21 2008
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EXAMPLE
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The MR-expansion of 1/5 using m=2 is {3,1,3,1,3,1,3,1,...}, because 1/5->2/5->4/5->8/5->3/5->6/5->1/5->... indicating that MR(1/5,2) begins {3,1,...} and has period length 2.
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CROSSREFS
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Cf. A136043, A136044.
Adjacent sequences: A136039 A136040 A136041 this_sequence A136043 A136044 A136045
Sequence in context: A046575 A154739 A136564 this_sequence A166044 A087707 A113011
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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), Dec 12 2007
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