A001133 Primes p such that the multiplicative order of 2 modulo p is (p-1)/3.

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

Author

N. J. A. Sloane

Keywords

• nonn

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

Crossrefs

Cf. A040028, A014752, A059914.

Cf. also A001134, A001135, A001136, A115586, A115591.

Programs

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

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 *)

PARI

forprime(p=3,10^4,if(znorder(Mod(2,p))==(p-1)/3,print1(p,", "))); \\ Joerg Arndt, May 17 2013

Extensions

More terms and better definition from Don Reble, Mar 11 2006