Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #34 Nov 01 2024 11:48:10
%S 7,17,23,41,47,71,79,97,103,137,167,191,193,199,239,263,271,311,313,
%T 359,367,383,401,409,449,463,479,487,503,521,569,599,607,647,719,743,
%U 751,761,769,809,823,839,857,863,887,929,967,977,983,991,1009,1031
%N Primes p such that the multiplicative order of 2 modulo p is (p-1)/2.
%C It appears that this is also the sequence of values of n for which the sum of terms of one period of the base-2 MR-expansion (see A136042) of 1/n equals (n-1)/2. An example appears in A155072 where one period of the base-2 MR-expansion of 1/17 is shown to be {5,1,1,1} with sum 8=(17-1)/2. - _John W. Layman_, Jan 19 2009
%C If p is a term of this sequence, then 2 is a quadratic residue module p, so p == 1, 7 (mod 8). - _Jianing Song_, Nov 01 2024
%H Klaus Brockhaus, <a href="/A115591/b115591.txt">Table of n, a(n) for n=1..1000</a>
%t fQ[n_] := 1 + 2 MultiplicativeOrder[2, n] == n; Select[ Prime@ Range@ 174, fQ]
%o (Magma) [ p: p in PrimesUpTo(1031) | r eq 1 and Order(R!2) eq q where q,r is Quotrem(p,2) where R is ResidueClassRing(p) ]; // _Klaus Brockhaus_, Dec 02 2008
%o (PARI) r=2;forprime(p=3,1500,z=(p-1)/znorder(Mod(r,p));if(z==2,print1(p,", "))); \\ _Joerg Arndt_, Jan 12 2011
%Y Cf. A001122, A001133.
%Y Cf. A136042, A155072. - _John W. Layman_, Jan 19 2009
%K nonn
%O 1,1
%A _Don Reble_, Mar 11 2006