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 A233930 #16 Sep 27 2014 16:03:29
%S A233930 3,7,17,31,127,257,3583,5119,6143,8191,65537,131071,524287,7340033,
%T A233930 14680063,104857601,109051903,167772161,469762049,2013265921,
%U A233930 2147483647,21474836479,51539607551,206158430209,824633720831,2748779069441,6597069766657,26388279066623
%N A233930 Primes p that give record exponents of 2 in p^2 - 1 (A091282).
%C A233930 Among these terms, we find the first Mersenne primes (A000668), and some Fermat numbers (A000215).
%H A233930 Hiroaki Yamanouchi, <a href="/A233930/b233930.txt">Table of n, a(n) for n = 1..100</a>
%e A233930 3^2 - 1 = 8 = 2^3. 5 does not beat this record with 5^2 - 1 = 24 = 2^3 * 3.
%e A233930 7^2 - 1 = 48 = 2^4 * 3, so 7 sets the next record, which stands through 11 and 13.
%e A233930 17^2 - 1 = 288 = 2^5 * 3^2.
%o A233930 (PARI) lista(nn) = {r = 0; forprime (n=1, nn, v = valuation(n^2-1, 2); if (v > r, r = v; print1(n, ", ")));}
%K A233930 nonn
%O A233930 1,1
%A A233930 _Michel Marcus_, Dec 20 2013
%E A233930 a(22)-a(28) from _Hiroaki Yamanouchi_, Sep 27 2014