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 A001133 Primes p such that the multiplicative order of 2 modulo p is (p-1)/3. (Formerly M5283 N2299) 18
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES 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). LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A040028, A014752, A059914. Cf. also A001134, A001135, A001136, A115586, A115591. Sequence in context: A106923 A115586 A294717 * A292578 A139969 A142055 Adjacent sequences: A001130 A001131 A001132 * A001134 A001135 A001136 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms and better definition from Don Reble, Mar 11 2006 STATUS approved

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Last modified August 13 18:32 EDT 2024. Contains 375144 sequences. (Running on oeis4.)