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

1,4

Links

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

Example

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.

Mathematica

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 *)

Prog

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

Crossrefs

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

Cf. A000040, A010051.

Sequence in context: A242849 A072917 A319861 * A230206 A285117 A135910

Adjacent sequences: A114263 A114264 A114265 * A114267 A114268 A114269

Keyword

easy,nonn

Author

Lei Zhou, Nov 20 2005

Extensions

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

Status

approved