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 A097443 Half-period primes, i.e., primes p for which the decimal expansion of 1/p has period (p-1)/2. 8
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Or, primes p for which 10 has multiplicative order (p-1)/2. - Robert Israel, Jul 15 2016 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 (Terms 2..1001 from T. D. Noe.) Makoto Kamada, Factorizations of 11...11 (Repunit). EXAMPLE 13 is a half-period prime because 1/13 = 0.076923076923076923076923... i.e., has period 6, or (13-1)/2. MAPLE select(t -> isprime(t) and numtheory:-order(10, t) = (t-1)/2, [seq(t, t = 3..1000, 2)]); # Robert Israel, Jul 15 2016 MATHEMATICA 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 *) PROG (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 CROSSREFS Almost the same as A001914. Cf. A001913, A055628, A056157, A056210-A056217, A098680 Cf. also A000040, A007732, A006883, A097443, A097955. Sequence in context: A077717 A235265 A275081 * A248368 A171517 A179026 Adjacent sequences:  A097440 A097441 A097442 * A097444 A097445 A097446 KEYWORD nonn AUTHOR Julien Peter Benney (jpbenney(AT)ftml.net), Aug 23 2004 EXTENSIONS Edited (including prepending 3) by N. J. A. Sloane, Oct 19 2018 at the suggestion of Georg Fischer. STATUS approved

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Last modified October 14 12:29 EDT 2019. Contains 328006 sequences. (Running on oeis4.)