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 A152578 #10 Oct 04 2024 23:08:50 %S A152578 7,27,627,390627,152587890627,23283064365386962890627, %T A152578 542101086242752217003726400434970855712890627 %N A152578 a(n) = 5^(2^(n-1)) + 2. %C A152578 Except for the first term, these numbers are divisible by 3. This follows from the identity I: a^n-b^n = (a+b)(a^(n-1) - a^(n-2)b + ... + b^(n-1)) for odd values of n. In this example, by expanding the binomial (3+2)^(2^n)+2, we get 3h + 2^(2^n)+2 for some h. Now 2^(2^n)+2 = 2*(2^(2^n-1)+1). Since 2^n-1 is odd, by identity I, 3 divides 2^(2^n)+2 + 3h. Therefore 3 divides 5^(2^n)+2 for n > 0. %o A152578 (PARI) a(n) = 5^(2^(n-1)) + 2 %K A152578 nonn,easy %O A152578 1,1 %A A152578 _Cino Hilliard_, Dec 08 2008