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A097443
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Half-period primes, i.e., primes p for which the decimal expansion of 1/p has period (p-1)/2.
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17
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3, 13, 31, 43, 67, 71, 83, 89, 107, 151, 157, 163, 191, 197, 199, 227, 283, 293, 307, 311, 347, 359, 373, 401, 409, 431, 439, 443, 467, 479, 523, 557, 563, 569, 587, 599, 601, 631, 653, 677, 683, 719, 761, 787, 827, 839, 877, 881, 883, 911, 919, 929, 947, 991
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OFFSET
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1,1
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COMMENTS
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Primes p for which 10 has multiplicative order (p-1)/2. - Robert Israel, Jul 15 2016
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LINKS
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EXAMPLE
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13 is a half-period prime because 1/13 = 0.076923076923076923076923..., which has period 6, or (13-1)/2.
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MAPLE
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select(t -> isprime(t) and numtheory:-order(10, t) = (t-1)/2,
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MATHEMATICA
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f[n_Integer] := Block[{ds = Divisors[n - 1]}, (n - 1)/Take[ ds, Position[ PowerMod[ 10, ds, n], 1] [[1, 1]]] [[ -1]]]; Select[ Prime[ Range[4, 200]], f[ # ] == 2 &] (* Robert G. Wilson v, Sep 14 2004 *)
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PROG
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(PARI) is(n)= gcd(10, n)==1 && isprime(n) && znorder(Mod(10, n))==(n-1)/2 \\ Dana Jacobsen, Jul 19 2016
(Perl) use ntheory ":all"; forprimes { say if znorder(10, $_) == ($_-1)/2; } 1, 1000; # Dana Jacobsen, Jul 19 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Julien Peter Benney (jpbenney(AT)ftml.net), Aug 23 2004
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EXTENSIONS
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STATUS
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approved
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