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 A084563 #19 Feb 16 2025 08:32:49
%S A084563 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,38,40,44,52,56,62,68,98,
%T A084563 128
%N A084563 Even numbers having no more than three partitions into two odd primes.
%C A084563 A002375(a(n)/2) <= 3.
%C A084563 There are no other terms <= 30000. Could it be that no other terms exist? - _John W. Layman_, Jul 28 2003
%C A084563 There are no further terms < 100000. - _Harvey P. Dale_, Apr 17 2018
%H A084563 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition.</a>
%H A084563 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%t A084563 nn=10^2; ps=Boole[PrimeQ[Range[1,2*nn,2]]]; Select[Range[nn],Sum[ps[[i]]ps[[#-i+1]],{i,Ceiling[#/2]}]<=3&]*2 (* _Jayanta Basu_, May 25 2013 *)
%t A084563 p2Q[n_]:=Count[n-Prime[Range[2,PrimePi[n/2]]],_?PrimeQ]<4; Select[ 2*Range[70],p2Q] (* _Harvey P. Dale_, Apr 17 2018 *)
%Y A084563 Cf. A084562, A084564.
%K A084563 nonn,more
%O A084563 1,1
%A A084563 _Reinhard Zumkeller_, May 30 2003