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 A152583 #6 Oct 01 2013 21:35:28 %S A152583 13,123,14643,214358883,45949729863572163, %T A152583 2111377674535255285545615254209923, %U A152583 4457915684525902395869512133369841539490161434991526715513934826243 %N A152583 Numbers of the form 11^(2^n) + 2. %C A152583 Except for the first term, these numbers are divisible by 3. This follows from the binomial expansion of (9+2)^(2^n)+2 = 9h + 2^(2^n)+2. Now 2^(2^n)+2 can be written as 2*(2^(2^n-1)+1) and 2^(2^n-1)+1 is divisible by 3. This is evident from the identity, a^m+b^m = (a+b)(a^(m-1) - a(m-2)b + ... + b^(m-1)) for odd m and 2^n-1 is odd. %o A152583 (PARI) g(a,n) = if(a%2,b=2,b=1);for(x=0,n,y=a^(2^x)+b;print1(y",")) %K A152583 nonn %O A152583 1,1 %A A152583 _Cino Hilliard_, Dec 08 2008