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 A174682 #6 Oct 13 2012 00:24:05
%S A174682 1,2,6,9,12,13,15,16,19,20,25,27,28,30,33,34,37,40,46,48,51,52,53,55,
%T A174682 58,61,64,68,73,74,76,77,78,82,85,86,89,90,100,102,103,106,113,115,
%U A174682 117,124,128,130,132,134,138,145,146,148,149,151,152,155,156,158,161,163,164
%N A174682 Positive integers which cannot be represented as half-sums (averages) of two primes with prime subscripts.
%C A174682 _Jason Kimberley_ computed the first 733 positive integers which cannot be represented as the half sum of two primes with prime subscripts (A174682) as found using the first 998 values of A006450. From computing the first 20 thousand terms of A006450 (the 20000th term is 3118459), he shows the next value in the sequence of complements must be greater than 2907940. The PIP-Goldbach Conjecture is: every sufficiently large even number can be represented as the sum of two primes with prime subscripts.
%H A174682 Jason Kimberley, <a href="/A174682/b174682.txt">Table of n, a(n) for n = 1..733</a>
%F A174682 Complement of A174681. Complement of {(A006450(i) + A006450(j))/2} = Complement of {(A000040(A000040(i)) + A000040(A000040(j)))/2}.
%e A174682 a(1) = 1 and a(2) = 2 are in the sequence because they are smaller than the first half-sum (average) of two primes with prime subscripts 3 = (3 + 3)/2 because 3 is the first prime with prime subscript, p(2). a(3) = 6 because there is no such half-sum between (5 + 5)/2 = 5 and (3 + 11)/2 = 7.
%Y A174682 Cf. A000040, A006450, A174681.
%K A174682 easy,nonn
%O A174682 1,2
%A A174682 _Jonathan Vos Post_, Mar 26 2010