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 A336347 #21 Jan 05 2025 19:51:41 %S A336347 13,101,29,13,39877,41,13,37,18661,13,41,73,13,5719237,144341,13,29, %T A336347 89,13,353,41,13,64450569241,29,13,37,101,13,89,53,13,113,313,13,37, %U A336347 41,13,29,73,13,41,181,13,37,29,13,857,73,13,389,41,13,37 %N A336347 Least prime factor of 44745755^4*2^(4n+2) + 1. %C A336347 There are k such that k*2^m + 1 is not prime for any m (then k is called a Sierpiński number). Erdős once conjectured that for such a k, the smallest prime factor of k*2^m + 1 would be bounded as m tends to infinitiy. The proven Sierpiński number k=44745755^4 is thought to be the first counterexample to this conjecture. %C A336347 This sequence is either unbounded (in which case 44745755^4 is in fact a counterexample) or periodic. %C A336347 a(229) <= 3034663491871541. - _Chai Wah Wu_, Aug 09 2020 %H A336347 Jeppe Stig Nielsen, <a href="/A336347/b336347.txt">Table of n, a(n) for n = 0..228</a> %H A336347 M. Filaseta et al., <a href="https://doi.org/10.1016/j.jnt.2008.02.004">On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture</a>, Journal of Number Theory, Volume 128, Issue 7 (July 2008), pp. 1916-1940. %H A336347 Anatoly S. Izotov, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/33-3/izotov.pdf">A Note on Sierpinski Numbers</a>, Fibonacci Quarterly (1995), pp. 206-207. %Y A336347 Cf. A020639, A076336, A213353, A258091, A336943. %K A336347 nonn %O A336347 0,1 %A A336347 _Jeppe Stig Nielsen_, Jul 19 2020