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A028416
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Primes p such that the decimal expansion of 1/p has a periodic part of even length.
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13
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7, 11, 13, 17, 19, 23, 29, 47, 59, 61, 73, 89, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 193, 197, 211, 223, 229, 233, 241, 251, 257, 263, 269, 281, 293, 313, 331, 337, 349, 353, 367, 373, 379, 383, 389, 401, 409, 419, 421, 433
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OFFSET
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1,1
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COMMENTS
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Primes whose reciprocals have even period length.
Primes p such that the order of 10 mod p is even. - Joerg Arndt, Mar 04 2014
Let (d(i): 1<=i<=2*K) be the period of the decimal expansion of 1/a(n), K=A002371(A049084(a(n)))/2, then d(i) + d(i+K) = 9 for i with 1<=i<=K, or, equivalently: u + v = 10^K - 1 with u = Sum_{i=1..K} d(i)*10^(K-i) and v = Sum_{i=1..K} d(i+K)*10^(K-i). - Reinhard Zumkeller, Oct 05 2008
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REFERENCES
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H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, "Die periodischen Dezimalbrueche". [Reinhard Zumkeller, Oct 05 2008]
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LINKS
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EXAMPLE
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(0,5,8,8,2,3,5,2,9,4,1,1,7,6,4,7) is the period of 1/17 (see A007450),
u = 5882352, v = 94117647: u + v = 99999999 = 10^8 - 1. (End)
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MAPLE
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st := ithprime(n):
if (modp(numtheory[order](10, st), 2) = 0) then
RETURN(st)
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MATHEMATICA
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Select[Prime[Range[4, 100]], EvenQ[Length[RealDigits[1/#][[1, 1]]]]&] (* Harvey P. Dale, Jul 07 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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Mario Velucchi (mathchess(AT)velucchi.it)
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EXTENSIONS
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STATUS
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approved
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