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 A331038 #29 Mar 28 2025 17:35:30 %S A331038 3,7,47,2207,4870847,23725150497407,562882766124611619513723647, %T A331038 9932388036497706472820043948129789713, %U A331038 102423269049837077051675109560558766898,7949236499829405891753012242872011683,119093374737774941856311333667076322210 %N A331038 Residues of the Lucas-Lehmer primality test for M(127) = 2^127 - 1. %C A331038 Since a(125) = 0, 2^127 - 1 = 170141183460469231731687303715884105727 is prime. This calculation was carried out by hand by Edouard Lucas. It took him 19 years from 1857 to 1876. The method works with a(0) = 3 since M(127) == 3 (mod 4). It also works with a(0) = 4 or a(0) = 10. %H A331038 Sergio Pimentel, <a href="/A331038/b331038.txt">Table of n,a(n) for n = 0..125</a> %H A331038 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Lucas-LehmerTest.html">Lucas Lehmer Test</a>. %H A331038 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lucas-Lehmer_primality_test">Lucas Lehmer Primality Test</a>. %F A331038 a(n) = (a(n-1)^2 - 2) mod (2^127-1) with a(0) = 3; a(125) is the final term. %t A331038 NestList[Mod[#^2-2,2^127-1]&, 3,10] (* _Stefano Spezia_, Mar 28 2025 *) %Y A331038 Cf. A000043, A000668, A001566, A095847. %Y A331038 Cf. also A129219, A129220, A129221, A129222, A129223, A129224, A129225. %K A331038 nonn,full,fini %O A331038 0,1 %A A331038 _Sergio Pimentel_, Jan 08 2020