A114266 - OEIS

%I #13 Aug 05 2017 11:29:53

%S 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,

%T 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,

%U 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

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

%H Reinhard Zumkeller, <a href="/A114266/b114266.txt">Table of n, a(n) for n = 1..10000</a>

%e n=1: 2*prime(1)+prime(1+1)=2*2+3=7 is prime, so a(1)=1;

%e n=2: 2*prime(2)+prime(2+1)=2*3+5=11 is prime, so a(2)=1;

%e ...

%e n=4: 2*prime(4)+prime(4+1)=2*7+11=25 is not prime

%e ...

%e 2*prime(4)+prime(4+3)=2*7+17=31 is prime, so a(4)=3.

%t 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}]

%t 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 *)

%o (Haskell)

%o a114266 n = head [m | m <- [1..],

%o                       a010051 (2 * a000040 n + a000040 (n + m)) == 1]

%o -- _Reinhard Zumkeller_, Oct 29 2013

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

%Y Cf. A000040, A010051.

%K easy,nonn

%O 1,4

%A _Lei Zhou_, Nov 20 2005

%E Edited definition to conform to OEIS style. - _N. J. A. Sloane_, Jan 08 2011