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a(0)=1; for n > 0, a(n) is the smallest odd number k such that (2 + Product_{j=a(n-1)..k-2, j odd} j) is prime.
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%I #12 Mar 06 2022 23:09:48

%S 1,3,5,7,15,17,19,23,27,29,31,41,43,49,69,71,73,77,79,87,89,93,97,113,

%T 119,123,127,139,145,149,151,175,179,181,187,195,197,199,213,221,223,

%U 227,229,233,245,251,263,267,269,271,285,323,375,385,389,395,397,559

%N a(0)=1; for n > 0, a(n) is the smallest odd number k such that (2 + Product_{j=a(n-1)..k-2, j odd} j) is prime.

%t t = {}; s = 1; c = 0; Do[s = s*i; c += 1; If[PrimeQ[s + 2], AppendTo[t, i - 2*(c - 1)]; s = 1; c = 0], {i, 1, 570, 2}]; t (* _Jayanta Basu_, Jul 07 2013 *)

%o (PARI) print1("1, "); p=1; c=3; for(n=1, 80, while(!isprime(p+2), p=p*c; c=c+2); print1(c", "); p=c; c=c+2)

%Y Cf. A073691, A073693.

%K nonn

%O 0,2

%A _Amarnath Murthy_, Aug 12 2002

%E Edited by _Ralf Stephan_, Mar 26 2003