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Smallest number m such that 2*prime(n) + prime(m) is a prime.
5

%I #8 Sep 30 2017 18:14:28

%S 2,2,4,2,2,2,4,2,3,3,4,2,2,2,6,3,2,4,2,3,4,2,2,11,3,6,3,2,2,4,2,2,6,3,

%T 2,3,2,2,11,3,4,2,2,2,5,2,2,2,6,6,3,4,4,11,2,3,2,4,2,4,2,8,3,4,5,2,4,

%U 2,2,14,3,3,2,2,8,2,4,2,8,5,8,5,2,14,6,3,4,2,2,6,2,11,5,2,2,4,2,3,2,2,2,6,5

%N Smallest number m such that 2*prime(n) + prime(m) is a prime.

%H Reinhard Zumkeller, <a href="/A114233/b114233.txt">Table of n, a(n) for n = 3..10000</a>

%e n=3: 2*prime(3)+prime(2)=2*5+3=13 is prime, so a(3)=2;

%e n=4: 2*prime(4)+prime(2)=2*7+3=17 is prime, so a(4)=2;

%e n=5: 2*prime(5)+prime(2)=2*11+3=25 is not prime

%e ...

%e 2*prime(5)+prime(4)=2*11+7=29 is prime, so a(5)=4.

%t Table[p1 = Prime[n1]; n2 = 1; p2 = Prime[n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; If[n2 >= n1, Print[n1]]; p2 = Prime[n2]]; n2, { n1, 3, 202}]

%t snm[n_]:=Module[{m=1,p=2Prime[n]},While[!PrimeQ[p+Prime[m]],m++];m]; Array[ snm,110,3] (* _Harvey P. Dale_, Sep 30 2017 *)

%o (Haskell)

%o a114233 n = head [m | m <- [1 .. n],

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

%o -- _Reinhard Zumkeller_, Oct 31 2013

%Y Cf. A073703, A114227, A114228, A114231.

%Y Cf. A010051, A000040.

%K easy,nonn

%O 3,1

%A _Lei Zhou_, Nov 20 2005

%E Edited definition to conform to OEIS style. - _Reinhard Zumkeller_, Oct 31 2013