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%I #22 Sep 03 2019 14:24:00
%S 3,3,3,7,7,37,37,163,671353,13243063,5906322013,12087247687
%N Smallest prime p such that p + 4^k is also prime for all k = 1, ..., n.
%C a(13) > 10^11. - _Donovan Johnson_, Dec 02 2009
%e Prime 3 generates the {3,7,19,67} exponential prime-chain of length 4 if the start is also counted.
%e The smallest "exponential 11-chain" starts with 13243063 as follows: 13243063, 13243067, 13243079, 13243127, 13243319, 13244087, 13247159, 13259447, 13308599, 13505207, 14291639.
%t Table[p = 2; While[Times @@ Boole@ PrimeQ[p + 4^Range@ n] != 1, p = NextPrime@ p]; p, {n, 10}] (* _Michael De Vlieger_, Mar 05 2017 *)
%o (PARI) okchain(n, p)=for (k=1, n, if (! isprime(p + 4^k), return (0));); return (1);
%o a(n) = {p = 2; while (! okchain(n, p), p = nextprime(p+1)); p;} \\ _Michel Marcus_, Dec 17 2013
%Y Cf. A023200, A049492-A049499.
%K nonn,more
%O 1,1
%A _Labos Elemer_
%E a(11)-a(12) from _Donovan Johnson_, Dec 02 2009