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A244570 Smallest prime p >= prime(n) such that p*prime(n)+2 is prime.

%I A244570 #21 Jan 19 2020 15:37:03
%S A244570 3,7,11,19,17,37,23,37,43,47,47,61,53,73,109,79,89,71,109,227,113,97,
%T A244570 139,137,127,149,127,131,283,137,139,181,173,151,167,191,173,193,193,
%U A244570 181,239,199,233,223,239,251,239,241,233,313,241,251,271,277,373,271
%N A244570 Smallest prime p >= prime(n) such that p*prime(n)+2 is prime.
%C A244570 See comment in A244572.
%H A244570 Jens Kruse Andersen, <a href="/A244570/b244570.txt">Table of n, a(n) for n = 2..10000</a>
%H A244570 V. Shevelev, <a href="https://arxiv.org/abs/0912.4006">Theorems on twin primes-dual case</a>, arXiv:0912.4006 [math.GM], 2009-2014. Sections 10,14.
%t A244570 a[n_] := For[p = Prime[n], True, p = NextPrime[p], If[PrimeQ[p Prime[n] + 2], Return[p]]];
%t A244570 Table[a[n], {n, 2, 60}] (* _Jean-François Alcover_, Nov 18 2018 *)
%t A244570 sp[n_]:=Module[{p=n},While[CompositeQ[p*n+2],p=NextPrime[p]];p]; Table[ sp[k],{k,Prime[Range[2,60]]}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 19 2020 *)
%o A244570 (PARI) s=[]; for(n=2, 100, p=q=prime(n); while(!isprime(p*q+2), p=nextprime(p+1)); s=concat(s, p)); s \\ _Colin Barker_, Jun 30 2014
%Y A244570 Cf. A242719, A242720.
%K A244570 nonn
%O A244570 2,1
%A A244570 _Vladimir Shevelev_, Jun 30 2014
%E A244570 More terms from _Peter J. C. Moses_, Jun 30 2014