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 A253280 #26 Mar 20 2025 18:07:39 %S A253280 3795,8925840,56446139763,568059199631352,4114789794835622912, %T A253280 75005556404194608192050,1744054672674891153663590400, %U A253280 49598666989151226098104244512918,1754638089240473418053140582402752512 %N A253280 Greatest k such that a polynomial f(x) with integer coefficients between 0 and k is irreducible if f(n) is prime. %C A253280 This is an extension of Cohn's irreducibility theorem, which is a(10) >= 9. %C A253280 Brillhart, Filaseta, & Odlyzko show that a(n) >= n-1; Filaseta shows that 10^30 < a(10) < 62 * 10^30. %C A253280 a(10) is due to Filaseta & Gross, a(8)-a(9) and a(11)-a(20) to Cole, and a(3)-a(7) to Dunn. Dunn proves that 7 <= a(2) <= 9, but its value is not known at present. %D A253280 J. Alexander. Irreducibility criteria for polynomials with nonnegative integer coefficients. Master's Thesis, University of South Carolina. 1987. Cited in Dunn 2014. %H A253280 Charles R Greathouse IV, <a href="/A253280/b253280.txt">Table of n, a(n) for n = 3..20</a> %H A253280 J. Brillhart, M. Filaseta, and A. Odlyzko, <a href="http://dx.doi.org/10.4153/CJM-1981-080-0">On an irreducibility theorem of A. Cohn</a>, Canad. J. Math. 33 (1981), pp. 1055-1059. %H A253280 Morgan Cole, <a href="https://scholarcommons.sc.edu/etd/1590">Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients</a> (2013). %H A253280 Scott Michael Dunn, <a href="https://scholarcommons.sc.edu/etd/2809">Explorations in Elementary and Analytic Number Theory</a> (2014). %H A253280 Michael Filaseta, <a href="http://dx.doi.org/10.4153/CJM-1988-013-6">Irreducibility criteria for polynomials with nonnegative coefficients</a>, Canad. J. Math. 40 (1988), pp. 339-351. %H A253280 Michael Filaseta and Samuel Gross, <a href="http://dx.doi.org/10.1016/j.jnt.2013.11.001">49598666989151226098104244512918</a>, J. Number Theory 137 (2014), pp. 16-49. %H A253280 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cohn%27s_irreducibility_criterion">Cohn's irreducibility criterion</a> %K A253280 nonn,nice %O A253280 3,1 %A A253280 _Charles R Greathouse IV_, Sep 30 2015