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A082603 a(n) is the first prime greater than a(n-1) such that a(n)*a(n-1)+2 is a prime, with a(1)=3.

%I A082603 #17 May 31 2021 16:05:32
%S A082603 3,5,7,11,19,23,37,47,73,227,241,251,271,317,367,563,607,641,727,761,
%T A082603 829,1091,1117,1223,1249,1451,1579,1601,1627,1721,1741,1787,1873,1877,
%U A082603 1933,1973,2017,2087,2137,2153,2287,2351,2521,2687,2707,2741,2851,3041,3121,3137,3181,3191,3361,3371,3457,3461,3541,3557,3607,3701,3877,3881,3907,3947
%N A082603 a(n) is the first prime greater than a(n-1) such that a(n)*a(n-1)+2 is a prime, with a(1)=3.
%H A082603 Harvey P. Dale, <a href="/A082603/b082603.txt">Table of n, a(n) for n = 1..1000</a>
%e A082603 a(3)=7, as 3 + 2 = 5, 3*5 + 2 = 17, 5*7 + 2 = 37, etc.
%t A082603 f[s_List] := Block[{p = pp = s[[-1]]}, While[p = NextPrime@p; !PrimeQ[ p*pp + 2],]; Append[s, p]]; Nest[f, {3}, 63] (* _Robert G. Wilson v_, Nov 08 2010 *)
%t A082603 fpg[p1_]:=Module[{p2=NextPrime[p1]},While[!PrimeQ[p1 p2+2],p2=NextPrime[ p2]];p2]; NestList[fpg,3,70] (* _Harvey P. Dale_, May 31 2021 *)
%o A082603 (PARI) { vp=vector(20); vp[1]=3; vc=1; vpt=3; print1(3","); for (vc=2,20, forprime (p=vp[vc-1]+1,10000, if (isprime(p*vp[vc-1]+2),vp[vc]=p;vpt*=p; print1(vp[vc]","); break))) }
%o A082603 (PARI) {v=3;print1(3",");forprime(p=5,10000,vp=v*p;if(isprime(vp+2),v=vp;print1(p",")))} \\ _Zak Seidov_, Nov 07 2010
%Y A082603 Cf. A039726, A082603, A096177.
%K A082603 easy,nonn
%O A082603 1,1
%A A082603 _Jon Perry_, May 23 2003
%E A082603 Definition and example corrected to match the sequence and PARI programming, two cross references added, and sequence extended by _Robert G. Wilson v_, Nov 08 2010