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 A229857 #31 Feb 16 2025 08:33:20 %S A229857 5043,2417158053779,5245728941618725066052704993134, %T A229857 215872416866954281715178071724040762825421437510476267629647193878371 %N A229857 Round(2^(m-n-2)/(m*log(8))), where m = 2^n - n - 2. %C A229857 a(9) has 145 digits and is too large to include. %C A229857 Conjecture: a(n) < f(n) = number of primes of the form k*2^(n+2) + 1 with k odd that exist between a = 2^(n+2) + 1 and b = floor((2^(2^n) + 1)/(3*2^(n+2) + 1)). %C A229857 For comparison, f(5) = 5746. %C A229857 If the extended Riemann hypothesis is true, then for every fixed epsilon > 0, f(n) = Li(b)/(a - 1) + O(b^(1/2 + epsilon)), where Li(b) = integral(2..b, dt/log(t)). %D A229857 P. Borwein, S. Choi, B. Rooney and A. Weirathmueller, The Riemann Hypothesis: A Resource for the Aficionado and Virtuoso Alike, Springer, Berlin, 2008, pp. 57-58. %H A229857 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a> %Y A229857 Cf. A000215, A016631, A023394, A046052. %K A229857 nonn,easy %O A229857 5,1 %A A229857 _Arkadiusz Wesolowski_, Oct 01 2013