%I #13 Mar 27 2013 11:48:50
%S 1,3,12,19,28,22,37,61,58,52,67,82,124,112,148,97,175,127,214,172,157,
%T 295,280,232,217,328,331,277,247,262,520,337,388,448,430,409,382,442,
%U 367,397,610,487,412,535,547,502,592,472,703,766,652,727,637,991,802
%N a(n) is the smallest positive integer such that 4n+2 can be partitioned into the sum of two primes in the form of 4k+3 in n ways
%C This is also the index of the first occurrence of n in A156642.
%H Lei Zhou, <a href="/A217697/b217697.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 12 because 50 = 4*12 + 2 is the smallest number of the form 4m + 2 which can be expressed as a sum of 2 primes of the form 4k + 3 in 3 ways (3 + 47, 7 + 43, and 19 + 31).
%e a(3) = 12 because A156642(12) = 3 while for 0<=n<12, A156642(n) < 3.
%t goal = 56; a = {}; Do[AppendTo[a, 0], {n, 1, goal}]; found = 0; k = 0; While[found < goal, k++; m = 4*k + 2; p1 = m + 1; ct = 0;
%t While[p1 = p1 - 4; p2 = m - p1; p1 >= p2, If[PrimeQ[p1] && PrimeQ[p2], ct++]]; If[ct <= goal, If[a[[ct]] == 0, a[[ct]] = k; found++]]]; a
%Y Cf. A156642, A214834, A016825, A000040, A002145, A217696.
%K nonn
%O 1,2
%A _Lei Zhou_, Mar 19 2013