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 A002587 M2386 N0948 #114 Jul 02 2025 16:01:54
%S A002587 2,3,5,3,17,11,13,43,257,19,41,683,241,2731,113,331,65537,43691,109,
%T A002587 174763,61681,5419,2113,2796203,673,4051,1613,87211,15790321,3033169,
%U A002587 1321,715827883,6700417,20857,26317,86171,38737,25781083,525313
%N A002587 Largest prime factor of 2^n + 1.
%C A002587 a(n) != 1 (mod n) for n = 3, 51, 141, 309, 321, 348, ... - _Giovanni Resta_ & _Thomas Ordowski_, Jan 05 2014
%C A002587 a(n) != 1 (mod n) iff a(m) = a(n) for some m < n. Then n = 3m for m = 1, 17, 47, 103, 107, 116, ... - _Thomas Ordowski_, Jan 08 2014
%D A002587 J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
%D A002587 M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 2, p. 85.
%D A002587 E. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math., 1 (1878), 184-239, 289-321.
%D A002587 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002587 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002587 Max Alekseyev, <a href="/A002587/b002587.txt">Table of n, a(n) for n = 0..1128</a> (terms 1..500 from T. D. Noe, terms 1037..1062 from Amiram Eldar, term 1108 from Tyler Busby)
%H A002587 J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H A002587 D. X. Charles, <a href="http://www.cs.wisc.edu/~cdx/LowerBound.pdf">The abc-conjecture and the largest prime factor of 2^n + 1</a>
%H A002587 Edouard Lucas, <a href="http://edouardlucas.free.fr/oeuvres/Theorie_des_fonctions_simplement_periodiques.pdf">Théorie des Fonctions Numériques Simplement Périodiques</a>, I", Amer. J. Math., 1 (1878), 184-240, 289-321. See pages 239 and 240.
%H A002587 Edouard Lucas, <a href="http://www.mathstat.dal.ca/FQ/Books/Complete/simply-periodic.pdf">The Theory of Simply Periodic Numerical Functions</a>, Fibonacci Association, 1969. English translation of article "Théorie des Fonctions Numériques Simplement Périodiques, I", Amer. J. Math., 1 (1878), 184-240.
%H A002587 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%F A002587 Charles proves that a(n) >> n^(4/3) infinitely often under the abc conjecture, and reports that Andrew Granville has improved this to a(n) >> n^2. - _Charles R Greathouse IV_, Apr 29 2013
%F A002587 a(n) = A006530(A000051(n)). - _Vincenzo Librandi_, Jul 12 2016
%t A002587 Table[FactorInteger[2^n + 1][[-1, 1]], {n, 0, 30}] (* _Vincenzo Librandi_, Jul 12 2016 *)
%o A002587 (Magma) [Maximum(PrimeDivisors(2^n+1)): n in [0..40]]; // _Vincenzo Librandi_, Jul 12 2016
%o A002587 (PARI) a(n)=my(f=factor(2^n+1)[,1]); f[#f] \\ _Charles R Greathouse IV_, Jul 12 2016
%Y A002587 Cf. A000051, A002586, A006530.
%Y A002587 Cf. similar sequences listed in A274903.
%K A002587 nonn
%O A002587 0,1
%A A002587 _N. J. A. Sloane_
%E A002587 More terms from _James Sellers_, Jul 06 2000
%E A002587 Offset 0, a(0) = 2 from _Vincenzo Librandi_, Jul 12 2016