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 A109440 #14 Jan 05 2020 05:38:47
%S A109440 2,6,8,14,16,18,20,26,30,42,108,132,234,264,288,354,504,1920,2010,5040
%N A109440 Even numbers k such that exactly half of the primes p with p <= k/2 give k-p also a prime.
%C A109440 Let k be an even integer. Let PrimeP be the set of prime partition points {p,q} such that p + q = k, p and q are prime and p <= q. Let CompP be the set of composite partition points {p,q} such that p + q = k, p is prime, q is composite and p <= q. Sequence gives value of k such that the size of the two sets PrimeP and CompP are equal.
%C A109440 Even numbers k such that 2*A045917(k/2) = A000720(k/2). - _Andrew Howroyd_, Jan 02 2020
%e A109440 The number k = 30 is included because the two sets PrimeP={{7,23},{11,19},{13,17}} and CompP={{2,28},{3,27},{5,25}} have the same number of elements.
%o A109440 (PARI)
%o A109440 d(n)={my(s=0); forprime(p=2, n, s+=if(isprime(2*n-p), 1, -1)); s}
%o A109440 { for(n=1, 10^4/2, if(d(n)==0, print1(2*n, ", "))) } \\ _Andrew Howroyd_, Jan 02 2020
%Y A109440 Cf. A000720, A045917, A109885.
%K A109440 nonn,more
%O A109440 1,1
%A A109440 Gilmar Rodriguez Pierluissi (gilmarlily(AT)yahoo.com), Aug 26 2005
%E A109440 Name edited and a(13)-a(20) from _Andrew Howroyd_, Jan 02 2020