This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115591 #34 Nov 01 2024 11:48:10
%S A115591 7,17,23,41,47,71,79,97,103,137,167,191,193,199,239,263,271,311,313,
%T A115591 359,367,383,401,409,449,463,479,487,503,521,569,599,607,647,719,743,
%U A115591 751,761,769,809,823,839,857,863,887,929,967,977,983,991,1009,1031
%N A115591 Primes p such that the multiplicative order of 2 modulo p is (p-1)/2.
%C A115591 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 A115591 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 A115591 Klaus Brockhaus, <a href="/A115591/b115591.txt">Table of n, a(n) for n=1..1000</a>
%t A115591 fQ[n_] := 1 + 2 MultiplicativeOrder[2, n] == n; Select[ Prime@ Range@ 174, fQ]
%o A115591 (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 A115591 (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 A115591 Cf. A001122, A001133.
%Y A115591 Cf. A136042, A155072. - _John W. Layman_, Jan 19 2009
%K A115591 nonn
%O A115591 1,1
%A A115591 _Don Reble_, Mar 11 2006