A001136 Primes p such that the multiplicative order of 2 modulo p is (p-1)/6. (Formerly M5221 N2271)

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

1,1

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)/6, Sow[p]]]][[2, 1]] (* Jean-François Alcover, Dec 10 2015, adapted from PARI *)

Prog

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

Crossrefs

Cf. A001133.

Sequence in context: A183784 A042874 A221448 * A256172 A142939 A229018

Adjacent sequences: A001133 A001134 A001135 * A001137 A001138 A001139

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved