Search: id:A007732
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%I A007732
%S A007732 1,1,1,1,1,1,6,1,1,1,2,1,6,6,1,1,16,1,18,1,6,2,22,1,1,6,3,6,28,1,15,1,
%T A007732 2,16,6,1,3,18,6,1,5,6,21,2,1,22,46,1,42,1,16,6,13,3,2,6,18,28,58,1,60,
%U A007732 15,6,1,6,2,33,16,22,6,35,1,8,3,1,18,6,6,13,1,9,5,41,6,16,21,28,2,44,1
%N A007732 Period of decimal representation of 1/n.
%C A007732 Appears to be a divisor of A007733*A007736. - Henry Bottomley (se16(AT)btinternet.com), 
               Dec 20 2001
%C A007732 Primes p such that a(p)=p-1 are in A001913. [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), 
               Nov 13 2008]
%D A007732 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 
               1996, pp. 159 etc.
%H A007732 T. D. Noe, <a href="b007732.txt">Table of n, a(n) for n=1..1000</a>
%H A007732 <a href="Sindx_1.html#1overn">Index entries for sequences related to 
               decimal expansion of 1/n</a>
%F A007732 Note that if n=r*s where r is a power of 2 and s is odd then a(n)=a(s). 
               Also if n=r*s where r is a power of 5 and s is not divisible by 5 
               then a(n) = a(s). So we just need a(n) for n not divisible by 2 or 
               5. This is the smallest number m such that n divides 10^m - 1; m 
               is a divisor of phi(n), where phi = A000010.
%F A007732 phi(n) = n-1 only if n is prime and since a(n) divides phi(n), a(n) can 
               only equal n-1 if n is prime. - Scott Hemphill (hemphill(AT)alumni.caltech.edu), 
               Nov 23 2006
%F A007732 a(n)=a(A132740(n)); a(A132741(n))=a(A003592(n))=1. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Aug 27 2007
%o A007732 (PARI) A007732(n,amax)={ if( n % 2== 0, return(A007732(n/2,amax)) ; ) 
               ; if( n % 5== 0, return(A007732(n/5,amax)) ; ) ; for(m=1,amax, if( 
               (10^m-1) % n == 0, return(m) ; ) ; ) ; return(-1) ; } { for(n=1,100, 
               print(n," ",A007732(n,500)) ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 30 2006
%Y A007732 Cf. A121341, A066799, A121090.
%Y A007732 A001913 [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Nov 13 
               2008]
%Y A007732 Sequence in context: A080219 A040037 A009194 this_sequence A126795 A064793 
               A034460
%Y A007732 Adjacent sequences: A007729 A007730 A007731 this_sequence A007733 A007734 
               A007735
%K A007732 nonn,base,easy,nice
%O A007732 1,7
%A A007732 N. J. A. Sloane (njas(AT)research.att.com), Hal Sampson [ hals(AT)easynet.com 
               ]
%E A007732 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 05 2000

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