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 A067319 #13 Feb 23 2021 13:06:24
%S A067319 1,2,3,4,5,6,8,10,12
%N A067319 Numbers n such that phi(n)^phi(n)+1 is prime.
%C A067319 It is conjectured that the sequence of Fermat primes (A019434) is complete; if so then this sequence is complete:
%C A067319 Suppose that x is a positive integer for which x^x+1 is prime. If x has an odd prime factor p, then x^x + 1 = (x^(x/p))^p + 1 is divisible by x^(x/p) + 1, so it is not prime. So x must be a power of 2. Hence x^x is also a power of 2, so x^x+1 is a Fermat prime.
%C A067319 If there are no Fermat primes beyond the known ones (as is widely believed), then x must be 1, 2, or 4. Letting x=phi(n), it is easy to see that n must be one of the numbers listed. - _Dean Hickerson_, Feb 11 2002
%e A067319 Cases n=1-12 are based on the primes 2, 5, 257.
%t A067319 ephiQ[n_]:=Module[{eph=EulerPhi[n]},PrimeQ[eph^eph+1]]; Select[ Range[ 20],ephiQ] (* _Harvey P. Dale_, Feb 23 2021 *)
%o A067319 (PARI) isok(n) = isprime(eulerphi(n)^eulerphi(n) + 1); \\ _Michel Marcus_, Oct 07 2013
%Y A067319 Cf. A063439, A000010.
%K A067319 nonn
%O A067319 1,2
%A A067319 _Labos Elemer_, Jan 15 2002