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 A238554 #29 Oct 20 2023 17:20:47
%S A238554 1,1,1,5,1,11,3,9,1,35,15,39,3,39,63,35,1,149,3,419,7,221,25,155,73,
%T A238554 735,69,29,193,261,3,135,81,149,85,125,117,809,303,509,27,699,325,29,
%U A238554 27,285,639,65,61,1911,639,165,295,1295,163,905,175,75,1593,249
%N A238554 Smallest k such that k + 2^n and k*2^n + 1 are both prime.
%C A238554 If a(n) = 1, then the two primes are the same and they are Fermat primes. - _Michel Marcus_, Mar 01 2014
%H A238554 Giovanni Resta, <a href="/A238554/b238554.txt">Table of n, a(n) for n = 0..500</a>
%e A238554 5 is in this sequence because 5 + 2^3 = 13 and 5*2^3 + 1 = 41 are both prime.
%t A238554 Table[Module[{k=1,c=2^n},While[!AllTrue[{c+k,k c+1},PrimeQ],k++];k],{n,0,60}] (* _Harvey P. Dale_, Oct 20 2023 *)
%o A238554 (PARI) a(n) = {k = 1;while (!(isprime(k + 2^n) && isprime(k*2^n + 1)), k++); k;} \\ _Michel Marcus_, Mar 01 2014
%Y A238554 Cf. A019434 (Fermat primes).
%K A238554 nonn
%O A238554 0,4
%A A238554 _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Feb 28 2014
%E A238554 a(15) corrected and a(24) from _Michel Marcus_, Mar 01 2014
%E A238554 Missing term and a(25)-a(59) from _Giovanni Resta_, Mar 01 2014