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A007732
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Period of decimal representation of 1/n.
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21
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Appears to be a divisor of A007733*A007736. - Henry Bottomley (se16(AT)btinternet.com), Dec 20 2001
Primes p such that a(p)=p-1 are in A001913. [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Nov 13 2008]
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REFERENCES
| J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, pp. 159 etc.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences related to decimal expansion of 1/n
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FORMULA
| 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.
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
a(n)=a(A132740(n)); a(A132741(n))=a(A003592(n))=1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 27 2007
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MATHEMATICA
| DigitCycleLength[r_Rational, b_Integer?Positive]:=MultiplicativeOrder[b, FixedPoint[Quotient[ #, GCD[ #, b]]&, Denominator[r]]]; Table[If[n<2, 1, DigitCycleLength[1/n, 10]], {n, 5!}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 29 2010]
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PROG
| (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
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CROSSREFS
| Cf. A121341, A066799, A121090.
A001913 [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Nov 13 2008]
Sequence in context: A080219 A040037 A009194 * A126795 A064793 A034460
Adjacent sequences: A007729 A007730 A007731 * A007733 A007734 A007735
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KEYWORD
| nonn,base,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Hal Sampson [ hals(AT)easynet.com ]
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 05 2000
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