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A115591
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Primes p such that the multiplicative order of 2 modulo p is (p-1)/2.
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13
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7, 17, 23, 41, 47, 71, 79, 97, 103, 137, 167, 191, 193, 199, 239, 263, 271, 311, 313, 359, 367, 383, 401, 409, 449, 463, 479, 487, 503, 521, 569, 599, 607, 647, 719, 743, 751, 761, 769, 809, 823, 839, 857, 863, 887, 929, 967, 977, 983, 991, 1009, 1031
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It appears that this is also the sequence of values of n for which the sum of terms of one period of the base-2 MR-expansion (see A136042) of 1/n equals (n-1)/2. An example appears in A155072 where one period of the base-2 MR-expansion of 1/17 is shown to be {5,1,1,1) with sum 8=(17-1)/2. [From John W. Layman (layman(AT)math.vt.edu), Jan 19 2009]
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LINKS
| Klaus Brockhaus, Table of n, a(n) for n=1..1000 [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 02 2008]
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MATHEMATICA
| fQ[n_] := 1 + 2 MultiplicativeOrder[2, n] == n; Select[ Prime@ Range@ 174, fQ]
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PROG
| (MAGMA) [ p: p in PrimesUpTo(1031) | r eq 1 and Order(R!2) eq q where q, r is Quotrem(p, 2) where R is ResidueClassRing(p) ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 02 2008]
(PARI) r=2; forprime(p=3, 1500, z=(p-1)/znorder(Mod(r, p)); if(z==2, print1(p, ", "))); [From Joerg Arndt, Jan 12 2011]
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CROSSREFS
| Cf. A001122, A001133.
Cf. A136042, A155072. [From John W. Layman (layman(AT)math.vt.edu), Jan 19 2009]
Sequence in context: A165353 A048976 A088546 * A026349 A057183 A076293
Adjacent sequences: A115588 A115589 A115590 * A115592 A115593 A115594
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KEYWORD
| nonn
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AUTHOR
| Don Reble (djr(AT)nk.ca), Mar 11 2006
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