A114232 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.

2, 10, 5, 14, 22, 35, 41, 26, 17, 92, 170, 79, 190, 43, 164, 240, 175, 590, 94, 236, 446, 1004, 279, 920, 409, 971, 646, 1088, 502, 449, 1219, 1263, 2049, 1541, 2191, 915, 3727, 1886, 1394, 4506, 5014, 1524, 1181, 6323, 888, 3995, 4033, 6625, 9664, 13733

Offset: 1

Author

Lei Zhou, Nov 20 2005

Keywords

• nonn

Comments

Shows the first 204 items; Sequenced defined for all k>=1; Sequence the first appearance of k in A114231

Examples

			k=1: Prime[2]+2*Prime[2-1]=3+2*2=7 is prime, so n(1)=2;
k=2: Prime[10]+2*Prime[10-2]=29+2*19=67 is prime, so n(2)=10;
while
Prime[3]+2*Prime[3-1]=5+2*3=11 is prime, not count according to the definition
		

Crossrefs

Cf. A114227, A114230, A114231.

Programs

Mathematica

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]];