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%I #3 Mar 31 2012 10:23:47
%S 2,10,9,7,8,40,80,28,34,73,52,174,86,105,127,161,326,225,356,154,245,
%T 394,362,350,279,586,846,321,929,1822,1683,1208,1091,2025,947,2108,
%U 1361,3181,372,2774,1898,3785,3676,2194,6447,2919,3590,7092,4955,2474,19409
%N n(k) is the minimum number that require at least k to make Prime[n]+2*Prime[n+k] a prime.
%e Prime[2]+2*Prime[2+1]=3+2*5=13 is prime, so n(1)=2;
%e Prime[3]+2*Prime[3+1]=5+2*7=19 is prime, not counted;
%e ...
%e Prime[7]+2*Prime[7+4]=17+2*31=79 is prime, so n(4)=7;
%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, A073703, A114235, A114262, A114229, A114232, A114234, A114237, A114263.
%K nonn
%O 1,1
%A _Lei Zhou_, Nov 20 2005
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