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 A119550 #10 Sep 16 2024 14:26:45
%S A119550 2,5,19,263,65551
%N A119550 Prime numbers of the form 2^(2^k) + 2^k - 1.
%F A119550 Define F(n) = 2^(2^n)+1 = n-th Fermat number, M(n) = 2^n-1 = the n-th Mersenne number. Then we are considering the numbers f(n) = F(n)+M(n)-1 = 2^(2^n) + 2^n - 1 (cf. A119563).
%e A119550 F(2)= 2^(2^2)+1 = 17, M(2) = 2^2-1 = 3, F(2)+ M(2)-1 = 19 is prime, so 2 is a member.
%t A119550 Select[Table[2^(2^k)+2^k-1,{k,0,10}],PrimeQ] (* _James C. McMahon_, Sep 15 2024 *)
%o A119550 (PARI) fmp3(n)=for(x=0,n,y=2^(2^x)+2^x-1;if(ispseudoprime(y),print1(y",")))
%Y A119550 Cf. A119563, A119564.
%K A119550 nonn,more,less
%O A119550 1,1
%A A119550 _Cino Hilliard_, May 31 2006
%E A119550 Edited by _N. J. A. Sloane_, Jun 03 2006
%E A119550 Definition corrected by _Stefan Steinerberger_, Jun 10 2007