A001133 - OEIS

%I M5283 N2299 #30 Sep 08 2022 08:44:28

%S 43,109,157,229,277,283,307,499,643,691,733,739,811,997,1021,1051,

%T 1069,1093,1459,1579,1597,1627,1699,1723,1789,1933,2179,2203,2251,

%U 2341,2347,2749,2917,3163,3181,3229,3259,3373,4027,4339,4549,4597,4651,4909,5101,5197,5323,5413,5437,5653,6037

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

%D M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 59.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001133/b001133.txt">Table of n, a(n) for n = 1..1000</a>

%t 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 *)

%o (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

%o (PARI) forprime(p=3,10^4,if(znorder(Mod(2,p))==(p-1)/3,print1(p,", "))); \\ _Joerg Arndt_, May 17 2013

%Y Cf. A040028, A014752, A059914.

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

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms and better definition from _Don Reble_, Mar 11 2006