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A001133
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Primes p such that the multiplicative order of 2 modulo p is (p-1)/3.
(Formerly M5283 N2299)
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18
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43, 109, 157, 229, 277, 283, 307, 499, 643, 691, 733, 739, 811, 997, 1021, 1051, 1069, 1093, 1459, 1579, 1597, 1627, 1699, 1723, 1789, 1933, 2179, 2203, 2251, 2341, 2347, 2749, 2917, 3163, 3181, 3229, 3259, 3373, 4027, 4339, 4549, 4597, 4651, 4909, 5101, 5197, 5323, 5413, 5437, 5653, 6037
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OFFSET
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1,1
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REFERENCES
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M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 59.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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Reap[For[p = 2, p < 10^4, p = NextPrime[p], If[MultiplicativeOrder[2, p] == (p-1)/3, Sow[p]]]][[2, 1]] (* Jean-François Alcover, Dec 10 2015 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(4597) | r eq 1 and Order(R!2) eq q where q, r is Quotrem(p, 3) where R is ResidueClassRing(p) ]; // Klaus Brockhaus, Dec 02 2008
(PARI) forprime(p=3, 10^4, if(znorder(Mod(2, p))==(p-1)/3, print1(p, ", "))); \\ Joerg Arndt, May 17 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms and better definition from Don Reble, Mar 11 2006
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STATUS
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approved
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