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

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

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, A001134, A001136, A115586, A115591.

Programs

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

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 *)

PARI

forprime(p=3,10^5,if(znorder(Mod(2,p))==(p-1)/5,print1(p,", "))); \\ Joerg Arndt, May 17 2013

Extensions

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