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 A339344 #13 Oct 12 2023 09:51:27
%S A339344 3,5,17,257,65537,4294967311,1229782942255939601,
%T A339344 88962710886098567818446141338419231,
%U A339344 255302062200114858892457591448999891874349780170241684791167583265041
%N A339344 Lexicographically earliest sequence of odd primes such that the asymptotic density of the numbers which are divisible by at least one of these primes is 1/2.
%C A339344 Given a set of prime numbers P, finite or infinite, the set of numbers which are divisible by at least one of the primes in P has an asymptotic density Product_{p in P} (1 - 1/p). If P is finite, then this density is equal to 1/2 only when P = {2}. Otherwise, the density is 1/2 for infinitely many sets P. This sequence is the lexicographically earliest infinite sequence of such primes.
%C A339344 The first 5 terms are the Fermat primes (A019434).
%C A339344 a(10) = 7.455916... * 10^135 is too large to be included in the data section.
%H A339344 Amiram Eldar, <a href="/A339344/b339344.txt">Table of n, a(n) for n = 1..12</a>
%F A339344 a(1) = 3, a(n) = nextprime(r(n-1)/(r(n-1) - 1/2)), where r(n) = Product_{k=1..n-1} 1 - 1/a(n).
%F A339344 Product_{n=>1} (1 - 1/a(n)) = 1/2.
%t A339344 s = {}; r = 1; p = 3; Do[AppendTo[s, p]; r *= 1 - 1/p; p = NextPrime[r/(r - 1/2)], {9}]; s
%Y A339344 Cf. A000215, A019434, A080307, A125045, A262228, A339345.
%K A339344 nonn
%O A339344 1,1
%A A339344 _Amiram Eldar_, Nov 30 2020