A001136 Primes p such that the multiplicative order of 2 modulo p is (p-1)/6.

31, 223, 433, 439, 457, 727, 919, 1327, 1399, 1423, 1471, 1831, 1999, 2017, 2287, 2383, 2671, 2767, 2791, 2953, 3271, 3343, 3457, 3463, 3607, 3631, 3823, 3889, 4129, 4423, 4519, 4567, 4663, 4729, 4759, 5167, 5449, 5503, 5953, 6007, 6079, 6151, 6217, 6271, 6673, 6961, 6967, 7321

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. A001133.

Programs

Magma

[ p: p in PrimesUpTo(6079) | r eq 1 and Order(R!2) eq q where q,r is Quotrem(p,6) 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)/6, Sow[p]]]][[2, 1]] (* Jean-François Alcover, Dec 10 2015, adapted from PARI *)

PARI

forprime(p=3,10^4,if(znorder(Mod(2,p))==(p-1)/6,print1(p,", "))); \\ Joerg Arndt, May 17 2013

Extensions

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