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 A274903 #43 Mar 15 2025 14:07:07
%S A274903 2,5,17,13,257,41,241,113,65537,109,61681,2113,673,1613,15790321,1321,
%T A274903 6700417,26317,38737,525313,4278255361,14449,2931542417,30269,
%U A274903 22253377,268501,308761441,279073,54410972897,536903681,4562284561,384773,67280421310721
%N A274903 Largest prime factor of 4^n + 1.
%H A274903 Max Alekseyev, <a href="/A274903/b274903.txt">Table of n, a(n) for n = 0..583</a>
%H A274903 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.
%F A274903 a(n) = A006530(A052539(n)). - _Michel Marcus_, Jul 11 2016
%F A274903 a(2n) = A002590(n). a(2n+1) = A229747(n). - _R. J. Mathar_, Feb 28 2018
%F A274903 a(n) = A002587(2*n). - _Amiram Eldar_, Feb 01 2020
%e A274903 4^3 + 1 = 65 = 5*13, so a(3) = 13.
%t A274903 Table[FactorInteger[4^n + 1][[-1, 1]], {n, 0, 30}]
%o A274903 (Magma) [Maximum(PrimeDivisors(4^n+1)): n in [0..35]];
%o A274903 (PARI) a(n)=my(f=factor(4^n+1)[,1]); f[#f] \\ _Charles R Greathouse IV_, Jul 12 2016
%Y A274903 Cf. largest prime factor of k^n+1: A002587 (k=2), A074476 (k=3), this sequence (k=4), A074478 (k=5), A274904 (k=6), A227575 (k=7), A274905 (k=8), A002592 (k=9), A003021 (k=10), A062308 (k=11).
%Y A274903 Cf. A006530, A052539.
%K A274903 nonn
%O A274903 0,1
%A A274903 _Vincenzo Librandi_, Jul 11 2016
%E A274903 Terms to a(100) in b-file from _Vincenzo Librandi_, Jul 12 2016
%E A274903 a(101)-a(531) in b-file from _Amiram Eldar_, Feb 01 2020
%E A274903 a(532)-a(583) in b-file from _Max Alekseyev_, Apr 25 2022, Mar 15 2025