Search: id:A136042
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%I A136042
%S A136042 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,
%T A136042 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,
%U A136042 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
%N A136042 Base-2 MR-expansion of 1/29.
%C A136042 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.
%F A136042 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
%e A136042 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.
%Y A136042 Cf. A136043, A136044.
%Y A136042 Sequence in context: A046575 A154739 A136564 this_sequence A166044 A087707 
               A113011
%Y A136042 Adjacent sequences: A136039 A136040 A136041 this_sequence A136043 A136044 
               A136045
%K A136042 nonn
%O A136042 1,1
%A A136042 John W. Layman (layman(AT)math.vt.edu), Dec 12 2007

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