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 A334810 #18 Apr 24 2023 09:35:33
%S A334810 0,0,0,0,1,0,1,0,1,4,1,3,2,1,1,4,7,2,4,3,1,4,3,4,6,5,2,2,0,1,8,7,8,3,
%T A334810 8,5,5,7,5,6,7,2,8,4,3,1,7,14,10,7,4,6,3,7,8,11,14,8,6,5,3,8,14,10,7,
%U A334810 6,11,13,15,10,7,7,9,10,11,8,9,10,7,9,13,9,13,10,9,6,6,8,7,3,2,9,10,10,10,10,8,15,9,20
%N A334810 The number of even numbers between 4 and 2p that cannot be written as the sum of two primes less than or equal to the n-th prime number p.
%C A334810 This sequence is related to the Goldbach conjecture: any even number (m) greater than 4 can be written as the sum of two odd primes (i.e., m = p1 + p2). For any given prime number p, if the restriction (p1, p2 <= p) is applied, some even numbers less than 2p may not be written as the sum of two prime numbers. The prime numbers corresponding to a(n)=0 in this sequence are the seven prime numbers listed in A301776.
%H A334810 Ya-Ping Lu, <a href="/A334810/b334810.txt">Table of n, a(n) for n = 1..100000</a>
%e A334810 a(1)=0. The 1st prime is 2. Even number 4 can be written as 2+2.
%e A334810 a(2)=0. The 2nd prime is 3. Even numbers 4 and 6 can be written as: 4=2+2 and 6=3+3.
%e A334810 a(3)=0. The 3rd prime is 5. Even numbers between 4 and 10 are: 4=2+2, 6=3+3, 8=3+5, and 10=5+5.
%e A334810 a(5)=1. The 5th prime is 11. Among the 10 even numbers between 4 and 22, only 20 cannot be written as the sum of two primes <= 11.
%e A334810 a(10)=4. The 10th prime is 29. Four even numbers (44, 50, 54, and 56) between 4 and 58 cannot be written as the sum of two primes <= 29.
%t A334810 a[n_] := Block[{p = Prime[n], r = Prime@ Range@ n}, Sum[Boole[{} == IntegerPartitions[2 k, {2}, r]], {k, 2, p}]]; Array[a, 83] (* _Giovanni Resta_, May 12 2020 *)
%Y A334810 Cf. A301776 (prime numbers p with the property that all even numbers n (2 < n <= 2p) are the sum of two primes <= p).
%K A334810 nonn
%O A334810 1,10
%A A334810 _Ya-Ping Lu_, May 12 2020