%I #3 Mar 31 2012 10:23:47
%S 3,12,9,10,8,17,97,20,57,50,30,56,207,171,210,134,303,127,121,275,376,
%T 278,299,413,432,251,746,949,389,742,725,1790,1375,3605,783,1812,895,
%U 1257,2079,2962,4799,3456,6356,1701,5255,4669,5011,7164,3012,8361,11210
%N n(k) is the minimum n that requires at least k to make 2*Prime[n]+Prime[n-k] a prime.
%e 2*Prime[3]+Prime[3-1]=2*5+3=13 is prime, so n(1)=3;
%e 2*Prime[4]+Prime[4-1]=2*7+5=19 is prime, not counted
%e ...
%e 2*Prime[8]+Prime[8-1]=2*19+17=55 is not prime
%e 2*Prime[8]+Prime[8-2]=2*19+13=51 is not prime
%e 2*Prime[8]+Prime[8-3]=2*19+11=49 is not prime
%e ...
%e 2*Prime[8]+Prime[8-5]=2*19+5=43 is prime, so n(5)=8;
%t Do[n[k] = 0, {k, 1, 2000}]; ct = 0; nm = 0; n2 = 0; n1 = 3; p1 = 5; While[ct < 200, n2 = 1; p2 = Prime[n1 - n2]; \ While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 - n2]]; If[n[n2] == 0, n[ n2] = n1; If[n2 > nm, nm = n2]; If[n2 <= 200, ct++ ]; Print[Table[n[k], {k, 1, nm}]]]; n1++; p1 = Prime[n1]]
%Y Cf. A114227, A114230, A073703, A114229, A114232, A114234, A114235, A114236.
%K nonn
%O 1,1
%A _Lei Zhou_, Nov 20 2005