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 A007732 Period of decimal representation of 1/n. 36
 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; text; internal format)
 OFFSET 1,7 COMMENTS Appears to be a divisor of A007733*A007736. - Henry Bottomley, Dec 20 2001 Primes p such that a(p)=p-1 are in A001913. [Dmitry Kamenetsky, Nov 13 2008] When 1/n has a finite decimal expansion (namely, when n = 2^a*5^b), a(n) = 1 while A051626(n) = 0. - M. F. Hasler, Dec 14 2015 REFERENCES J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, pp. 159 etc. LINKS Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) Project Euler, Reciprocal cycles: Problem 26 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, Aug 27 2007 MATHEMATICA Table[r = n/2^IntegerExponent[n, 2]/5^IntegerExponent[n, 5]; MultiplicativeOrder[10, r], {n, 100}] (* T. D. Noe, Oct 17 2012 *) PROG (PARI) a(n)=znorder(Mod(10, n/2^valuation(n, 2)/5^valuation(n, 5))) \\ Charles R Greathouse IV, Jan 14 2013 (Sage) def a(n):     n = ZZ(n)     rad = 2**n.valuation(2) * 5**n.valuation(5)     return Zmod(n // rad)(10).multiplicative_order() [a(n) for n in range(1, 20)] # F. Chapoton, May 03 2020 CROSSREFS Cf. A121341, A066799, A121090, A001913, A084680. Sequence in context: A324544 A323160 A323166 * A237835 A126795 A334491 Adjacent sequences:  A007729 A007730 A007731 * A007733 A007734 A007735 KEYWORD nonn,base,easy,nice AUTHOR N. J. A. Sloane, Hal Sampson [ hals(AT)easynet.com ] EXTENSIONS More terms from James A. Sellers, Feb 05 2000 STATUS approved

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Last modified May 24 19:14 EDT 2020. Contains 334580 sequences. (Running on oeis4.)