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%I #4 Mar 31 2012 10:23:47
%S 2,10,5,14,22,35,41,26,17,92,170,79,190,43,164,240,175,590,94,236,446,
%T 1004,279,920,409,971,646,1088,502,449,1219,1263,2049,1541,2191,915,
%U 3727,1886,1394,4506,5014,1524,1181,6323,888,3995,4033,6625,9664,13733
%N n(k) is the minimum number of n that need at least another number of k to make Prime[n]+2*Prime[n-k]a prime.
%C Shows the first 204 items; Sequenced defined for all k>=1; Sequence the first appearance of k in A114231
%e k=1: Prime[2]+2*Prime[2-1]=3+2*2=7 is prime, so n(1)=2;
%e k=2: Prime[10]+2*Prime[10-2]=29+2*19=67 is prime, so n(2)=10;
%e while
%e Prime[3]+2*Prime[3-1]=5+2*3=11 is prime, not count according to the definition
%t Do[n[k] = 0, {k, 1, 2000}]; ct = 0; nm = 0; n2 = 0; n1 = 2; p1 = 3; While[ct < 200, n2 = 1; p2 = Prime[n1 - n2]; While[cp = p1 + 2*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, A114231.
%K nonn
%O 1,1
%A _Lei Zhou_, Nov 20 2005
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