A001135 Primes p such that the multiplicative order of 2 modulo p is (p-1)/5. (Formerly M5424 N2356)

251, 571, 971, 1181, 1811, 2011, 2381, 2411, 3221, 3251, 3301, 3821, 4211, 4861, 4931, 5021, 5381, 5861, 6221, 6571, 6581, 8461, 8501, 9091, 9461, 10061, 10211, 10781, 11251, 11701, 11941, 12541, 13171, 13381, 13421, 13781, 14251, 15541, 16091, 16141, 16451, 16661, 16691, 16811, 17291

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

Maple

q:= p-> isprime(p) and numtheory[order](2, p)=(p-1)/5:
select(q, [$2..20000])[];  # Alois P. Heinz, Dec 12 2023

Mathematica

Reap[For[p = 2, p <= 18000, p = NextPrime[p], If[ MultiplicativeOrder[2, p] == (p-1)/5, Sow[p]]]][[2, 1]] (* James C. McMahon, Dec 12 2023 *)

Prog

(Magma) [ p: p in PrimesUpTo(15541) | r eq 1 and Order(R!2) eq q where q, r is Quotrem(p, 5) where R is ResidueClassRing(p) ]; // Klaus Brockhaus, Dec 02 2008
(PARI) forprime(p=3, 10^5, if(znorder(Mod(2, p))==(p-1)/5, print1(p, ", "))); \\ Joerg Arndt, May 17 2013

Crossrefs

Cf. A001133, A001134, A001136, A115586, A115591.

Sequence in context: A142924 A346493 A107696 * A052232 A179231 A108833

Adjacent sequences: A001132 A001133 A001134 * A001136 A001137 A001138

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved