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 A118371 #12 Aug 09 2025 09:56:54
%S A118371 2,3,5,7,13,19,23,31,37,43,47,53,61,79,83,101,107,109,113,131,139,157,
%T A118371 167,199,211,251,269,281,283,293,307,313,337,383,401,421,431,439,449,
%U A118371 457,491,509,521,523,569,601,643,673,691,701,769,773,811,839,863,881
%N A118371 Fastest growing sequence of primes satisfying Goldbach's conjecture.
%C A118371 Although there are 78498 primes < 10^6, only 3030 primes are required to form all even numbers < 10^6. There are 10582, 36308 and 123139 of these primes less than 10^7, 10^8 and 10^9, respectively. The asymptotic density of these primes appears to be 0. The number of these primes < x is roughly 0.85 sqrt(x log(x)).
%C A118371 Assuming the strong form of Goldbach's conjecture, Granville proves that thin sets of primes exist such that every even number >2 is the sum of two members of the set. - _T. D. Noe_, Apr 26 2006
%H A118371 T. D. Noe, <a href="/A118371/b118371.txt">Table of n, a(n) for primes up to 10^6</a>
%H A118371 Andrew Granville, <a href="http://www.dms.umontreal.ca/~andrew/PDF/GoldbachFinal.pdf">Refinements of Goldbach's conjecture and the Generalized Riemann Hypothesis</a>
%H A118371 T. D. Noe, <a href="http://www.sspectra.com/math/A118371.txt">Terms up to 10^9 (1.3 MB)</a>
%t A118371 ps={2,3}; Do[pn=Select[2n-ps,PrimeQ]; If[Intersection[ps,pn]=={}, AppendTo[ps, Max[pn]]], {n,4,1000}]; Sort[ps]
%Y A118371 Cf. A105170 (primes unnecessary for Goldbach's conjecture).
%K A118371 nice,nonn
%O A118371 1,1
%A A118371 _T. D. Noe_, Apr 26 2006