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 A228943 #19 Mar 08 2014 22:46:22
%S A228943 0,0,1,1,1,3,4,5,6,12,14,18,22,39,51,68,83,112,184,251,315,431,527,
%T A228943 652,768,1011,1128,1305,1836,2344,3240,4082,4955,5725,8023,8723,10260,
%U A228943 11945,16771,21466,30280,38583,46645,54789,77430,85067,99199,120742,154753
%N A228943 Number of decompositions of highly composite numbers (A002182) into unordered sums of two primes.
%C A228943 a(n) = A045917(A002182(n)/2) for n>1.
%C A228943 Conjecture: (a) This sequence is strictly increasing beginning with n=5. (b) For all n>2, if p is the greatest prime with p<A002182(n)-1, then A002182(n)-p is prime. This is a strengthening of a conjecture regarding A117825. - _Jaycob Coleman_, Sep 08 2013
%e A228943 a(6)=3, since 24=5+19=7+17=11+13.
%o A228943 (PARI) nbd(n) = my(s); forprime(p=2, n\2, s+=isprime(n-p)); s;
%o A228943 lista(nn) = {last = 1; print1(nbd(last), ", "); forstep(n=2, nn, 2, if(numdiv(n)> last, last=numdiv(n); print1(nbd(n), ", ")););} \\ _Michel Marcus_, Sep 10 2013
%Y A228943 Cf. A116979, A117825.
%K A228943 nonn
%O A228943 1,6
%A A228943 _Jaycob Coleman_, Sep 08 2013
%E A228943 More terms from _Michel Marcus_, Sep 10 2013