A114237 n(k) is the minimum n that requires at least k to make 2*Prime[n]+Prime[n-k] a prime.

3, 12, 9, 10, 8, 17, 97, 20, 57, 50, 30, 56, 207, 171, 210, 134, 303, 127, 121, 275, 376, 278, 299, 413, 432, 251, 746, 949, 389, 742, 725, 1790, 1375, 3605, 783, 1812, 895, 1257, 2079, 2962, 4799, 3456, 6356, 1701, 5255, 4669, 5011, 7164, 3012, 8361, 11210

Offset: 1

Author

Lei Zhou, Nov 20 2005

Keywords

• nonn

Examples

			2*Prime[3]+Prime[3-1]=2*5+3=13 is prime, so n(1)=3;
2*Prime[4]+Prime[4-1]=2*7+5=19 is prime, not counted
...
2*Prime[8]+Prime[8-1]=2*19+17=55 is not prime
2*Prime[8]+Prime[8-2]=2*19+13=51 is not prime
2*Prime[8]+Prime[8-3]=2*19+11=49 is not prime
...
2*Prime[8]+Prime[8-5]=2*19+5=43 is prime, so n(5)=8;
		

Crossrefs

Cf. A114227, A114230, A073703, A114229, A114232, A114234, A114235, A114236.

Programs

Mathematica

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]]