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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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9
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Primes whose reciprocals have even period length.
A002371(A049084(a(n))) mod 2 == 0.
Not the same as A040121: a(33)=241 is not in A040121.
Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 05 2008: (Start)
Let (d(i): 1<=i<=2*K) be the period of 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(d(i)*10^(K-i):1<=i<=K) and v=SUM(d(i+K)*10^(K-i):1<=i<=K). (End)
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REFERENCES
| H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, 'Die periodischen Dezimalbrueche'. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 05 2008]
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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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EXAMPLE
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 05 2008: (Start)
(0,5,8,8,2,3,5,2,9,4,1,1,7,6,4,7) is the period of 1/17 (see A007450),
K = A002371(A049084(17))/2 = A002371(7)/2 = 16/2 = 8,
u = 5882352, v = 94117647: u + v = 99999999 = 10^8 - 1. (End)
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MAPLE
| A028416 := proc(n) local st:
st := ithprime(n):
if (modp(numtheory[order](10, st), 2) = 0) then
RETURN(st)
fi: end: seq(A028416(n), n=1..100); # - Jani Melik, Feb 24 2011
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MATHEMATICA
| Select[Prime[Range[4, 100]], EvenQ[Length[RealDigits[1/#][[1, 1]]]]&] (* From Harvey P. Dale, Jul 07 2011 *)
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PROG
| (PARI) forprime(p=7, 1e3, if(znorder(Mod(10, p))%2==0, print1(p", "))) \\ Charles R Greathouse IV, Feb 24, 2011
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CROSSREFS
| Cf. A087000.
Sequence in context: A135776 A067831 A086998 * A040121 A156114 A091554
Adjacent sequences: A028413 A028414 A028415 * A028417 A028418 A028419
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KEYWORD
| nonn,base
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AUTHOR
| Mario Velucchi (mathchess(AT)velucchi.it)
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EXTENSIONS
| More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 29 2003
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