This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049500 #33 May 13 2025 00:55:20
%S A049500 3,3,3,7,7,37,37,163,671353,13243063,5906322013,12087247687,
%T A049500 1523351345443,1523351345443,23631302781703
%N A049500 Smallest prime p such that p + 4^k is also prime for all k = 1, ..., n.
%C A049500 a(13) > 10^11. - _Donovan Johnson_, Dec 02 2009
%C A049500 All terms from a(4) satisfy p == 7 or 13 (mod 30); a(16) > 10^14. - _Mikk Heidemaa_, May 12 2025
%e A049500 Prime 3 generates the {3,7,19,67} exponential prime-chain of length 4 if the start is also counted.
%e A049500 The smallest "exponential 11-chain" starts with 13243063 as follows: 13243063, 13243067, 13243079, 13243127, 13243319, 13244087, 13247159, 13259447, 13308599, 13505207, 14291639.
%t A049500 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 A049500 (PARI) okchain(n, p)=for (k=1, n, if (! isprime(p + 4^k), return (0));); return (1);
%o A049500 a(n) = {p = 2; while (! okchain(n, p), p = nextprime(p+1)); p;} \\ _Michel Marcus_, Dec 17 2013
%Y A049500 Cf. A023200, A049492-A049499.
%K A049500 nonn,more
%O A049500 1,1
%A A049500 _Labos Elemer_
%E A049500 a(11)-a(12) from _Donovan Johnson_, Dec 02 2009
%E A049500 a(13)-a(15) from _Mikk Heidemaa_, May 12 2025