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 A091317 #35 Dec 19 2024 12:19:34
%S A091317 2,3,5,11,13,17,19,29,37,41,43,53,59,61,67,83,97,101,107,109,113,131,
%T A091317 137,139,149,157,163,173,179,181,193,197,211,227,229,241,251,257,269,
%U A091317 277,281,283,293,307,313,317,331,347,349,353,373,379,389,397,401,409,419,421,433
%N A091317 Primes p that divide 2^n+1 for some n.
%C A091317 From _Charles R Greathouse IV_, Feb 13 2009: (Start)
%C A091317 Essentially the same as A014662.
%C A091317 Also primes p for which p^2 divides 2^n+1 for some n. If p | 2^g + 1, then 2^g = kp - 1 for some k, so 2^gp = (kp - 1)^p = (-1)^p + (-1)^(p-1) * kp * (p choose 1) + ... and so 2^gp = -1 (mod p^2). (End)
%H A091317 T. D. Noe, <a href="/A091317/b091317.txt">Table of n, a(n) for n=1..1000</a>
%H A091317 Alexi Block Gorman, Tyler Genao, Heesu Hwang, Noam Kantor, Sarah Parsons, and Jeremy Rouse, <a href="http://arxiv.org/abs/1508.02464">The density of primes dividing a particular non-linear recurrence sequence</a>, arXiv:1508.02464 [math.NT], 2015 (see Introduction).
%H A091317 H. H. Hasse, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002295253">Über die Dichte der Primzahlen p, für die eine vorgegebene ganzrationale Zahl a != 0 von durch eine vorgegebene Primzahl l != 2 teilbarer bzw. unteilbarer Ordnung mod. p ist</a>, Math. Ann., 162 (1965), 74-76.
%H A091317 H. H. Hasse, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002296616">Über die Dichte der Primzahlen p, für die eine vorgegebene ganzrationale Zahl a != 0 von gerader bzw. ungerader Ordnung mod. p ist</a>, Math. Ann., 166 (1966), 19-23.
%H A091317 Eugen J. Ionascu, Florian Luca, and Thomas Merino, <a href="https://arxiv.org/abs/2412.10839">On the average value of the minimal Hamming multiple</a>, arXiv:2412.10839 [math.NT], 2024. See pp. 4, 17.
%H A091317 J. C. Lagarias, <a href="http://projecteuclid.org/euclid.pjm/1102706452">The set of primes dividing the Lucas numbers has density 2/3</a>, Pacific J. Math., 118. No. 2, (1985), 449-461.
%H A091317 C. Smyth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Smyth/smyth2.html">The terms in Lucas Sequences divisible by their indices</a>, JIS 13 (2010) #10.2.4.
%F A091317 Has density 17/24 (Hasse 1966).
%p A091317 2, op(select(t -> isprime(t) and numtheory:-order(2,t)::even, [seq(2*i+1, i=1..1000)])); # _Robert Israel_, Aug 12 2015
%t A091317 Join[{2}, Select[Prime[Range[100]], EvenQ[MultiplicativeOrder[2, #/ (2^IntegerExponent[#, 2])]]&]] (* _Jean-François Alcover_, Sep 02 2018 *)
%o A091317 (PARI) isA091317(p)=!bitand(znorder(Mod(2,p)),1) \\ _Charles R Greathouse IV_, Feb 13 2009
%Y A091317 Complement in primes of A014663.
%Y A091317 Cf. A014662. - _Charles R Greathouse IV_, Feb 13 2009
%K A091317 nonn
%O A091317 1,1
%A A091317 _N. J. A. Sloane_, Feb 21 2004