A114234 n(k) is the minimum n that requires at least k to make 2*Prime[n]+Prime[k] a prime.

3, 11, 5, 47, 17, 106, 64, 157, 133, 26, 236, 308, 72, 496, 122, 207, 152, 142, 197, 259, 514, 497, 1266, 1482, 2005, 2193, 1380, 964, 3662, 534, 4055, 667, 2513, 6083, 1794, 689, 3332, 5771, 3713, 4587, 3450, 12520, 5712, 3242, 10252, 18663, 11912, 25124

Offset: 2

Author

Lei Zhou, Nov 20 2005

Keywords

• nonn

Comments

Shows the first 204 items; The first appearance in A114233; Sequence is defined for all k>=2.

Examples

			k=2: 2*Prime[3]+Prime[2]=13 is prime, so n(2)=3;
2*Prime[4]+Prime[2]=17
2*Prime[5]+Prime[2]=25, ... 2*Prime[5]+Prime[4]=29 ==> n(4)=5;
		

Crossrefs

Cf. A073703, A114227, A114229, A114232, A114233.

Programs

Mathematica

Do[n[k] = 0, {k, 2, 2000}]; ct = 0; nm = 0; n2 = 0; n1 = 3; p1 = 5; While[ct < 200, n2 = 1; p2 = Prime[n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; p2 = Prime[n2]]; If[n[n2] == 0, n[ n2] = n1; If[n2 > nm, nm = n2]; If[n2 <= 201, ct++ ]; Print[Table[n[k], {k, 2, nm}]]]; n1++; p1 = Prime[n1]];