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 A334208 #18 Jan 29 2025 17:30:21
%S A334208 0,0,0,1,0,1,0,1,2,1,0,1,0,1,2,1,0,1,0,1,2,1,0,1,2,3,2,1,0,1,0,1,2,3,
%T A334208 2,1,0,1,2,1,0,1,0,1,2,1,0,1,2,3,2,1,0,1,2,3,2,1,0,1,0,1,2,3,2,1,0,1,
%U A334208 2,1,0,1,0,1,2,3,2,1,0,1,2,1,0,1,2,3,2,1,0,1,2,3,4,3,2,1,0,1,2,1,0,1,0,1,2
%N A334208 Number of partitions of 2n into two composite parts, (r,s), such that r and s have the same number of primes less than or equal to them.
%C A334208 Apparently a(n) = A051699(n) for n>=2. - _R. J. Mathar_, Apr 22 2020
%H A334208 Antti Karttunen, <a href="/A334208/b334208.txt">Table of n, a(n) for n = 1..65537</a>
%H A334208 <a href="/index/Par#part">Index entries for sequences related to partitions</a>.
%F A334208 a(n) = Sum_{i=2..n} [pi(i) = pi(2*n-i)] * (1 - c(i)) * (1 - c(2*n-i)), where [] is the Iverson bracket, pi is the prime counting function (A000720), and c is the prime characteristic (A010051).
%e A334208 a(9) = 2; 2*9 = 18 has two partitions into composite parts, (10,8) and (9,9), such that pi(10) = 4 = pi(8) and pi(9) = 4 = pi(9).
%t A334208 Table[Sum[KroneckerDelta[PrimePi[i], PrimePi[2 n - i]] (1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[2 n - i] + PrimePi[2 n - i - 1]), {i, 2, n}], {n, 100}]
%o A334208 (PARI) A334208(n) = sum(i=2,n,(!isprime(i) && !isprime(n+n-i) && primepi(i)==primepi(n+n-i))); \\ _Antti Karttunen_, Jan 29 2025
%Y A334208 Cf. A000720, A010051, A051699.
%K A334208 nonn,easy
%O A334208 1,9
%A A334208 _Wesley Ivan Hurt_, Apr 18 2020
%E A334208 Data section extended to a(105) by _Antti Karttunen_, Jan 29 2025