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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
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).
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
KEYWORD
nonn
EXTENSIONS
More terms and better definition from Don Reble, Mar 11 2006
STATUS
approved