A114263 -id:A114263 - cp's OEIS frontend

A114266 a(n) is the minimal number m that makes 2*prime(n)+prime(n+m) a prime.

1, 1, 1, 3, 3, 1, 1, 1, 3, 1, 2, 4, 6, 2, 6, 2, 1, 2, 5, 5, 2, 1, 2, 3, 5, 3, 1, 6, 1, 1, 8, 2, 4, 7, 1, 9, 3, 2, 9, 7, 5, 10, 4, 5, 1, 5, 5, 1, 1, 1, 8, 1, 1, 4, 6, 2, 1, 2, 12, 10, 1, 11, 8, 3, 11, 2, 2, 1, 4, 1, 7, 2, 3, 2, 11, 2, 3, 3, 3, 1, 1, 5, 2, 5, 1, 7, 3, 3, 4, 6, 4, 7, 4, 1, 9, 5, 3, 2, 4, 7, 2, 9, 2

Offset: 1

Lei Zhou, Nov 20 2005

			n=1: 2*prime(1)+prime(1+1)=2*2+3=7 is prime, so a(1)=1;
n=2: 2*prime(2)+prime(2+1)=2*3+5=11 is prime, so a(2)=1;
...
n=4: 2*prime(4)+prime(4+1)=2*7+11=25 is not prime
...
2*prime(4)+prime(4+3)=2*7+17=31 is prime, so a(4)=3.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A114227, A114230, A073703, A114235, A114262, A114228, A114231, A114233, A114236, A114263, A114265, A114267.

Cf. A000040, A010051.

a114266 n = head [m | m <- [1..],
                      a010051 (2 * a000040 n + a000040 (n + m)) == 1]
-- Reinhard Zumkeller, Oct 29 2013

Table[p1 = Prime[n1]; n2 = 1; p2 = Prime[n1 + n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 + n2]]; n2, {n1, 1, 200}]
mnm[n_]:=Module[{m=1,p=2Prime[n]},While[!PrimeQ[p+Prime[n+m]],m++];m]; Array[mnm,110] (* Harvey P. Dale, Aug 05 2017 *)

Edited definition to conform to OEIS style. - N. J. A. Sloane, Jan 08 2011

A114264 n(k) is the minimum number that require at least k to make Prime[n]+2*Prime[n+k] a prime.

Original entry on oeis.org

2, 10, 9, 7, 8, 40, 80, 28, 34, 73, 52, 174, 86, 105, 127, 161, 326, 225, 356, 154, 245, 394, 362, 350, 279, 586, 846, 321, 929, 1822, 1683, 1208, 1091, 2025, 947, 2108, 1361, 3181, 372, 2774, 1898, 3785, 3676, 2194, 6447, 2919, 3590, 7092, 4955, 2474, 19409

Offset: 1

Lei Zhou, Nov 20 2005

nonn

			Prime[2]+2*Prime[2+1]=3+2*5=13 is prime, so n(1)=2;
Prime[3]+2*Prime[3+1]=5+2*7=19 is prime, not counted;
...
Prime[7]+2*Prime[7+4]=17+2*31=79 is prime, so n(4)=7;

Cf. A114227, A114230, A073703, A114235, A114262, A114229, A114232, A114234, A114237, A114263.

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]]

cp's OEIS Frontend

A114266 a(n) is the minimal number m that makes 2*prime(n)+prime(n+m) a prime.

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