%I
%S 3,7,17,31,127,257,3583,5119,6143,8191,65537,131071,524287,7340033,
%T 14680063,104857601,109051903,167772161,469762049,2013265921,
%U 2147483647,21474836479,51539607551,206158430209,824633720831,2748779069441,6597069766657,26388279066623
%N Primes p that give record exponents of 2 in p^2  1 (A091282).
%C Among these terms, we find the first Mersenne primes (A000668), and some Fermat numbers (A000215).
%H Hiroaki Yamanouchi, <a href="/A233930/b233930.txt">Table of n, a(n) for n = 1..100</a>
%e 3^2  1 = 8 = 2^3. 5 does not beat this record with 5^2  1 = 24 = 2^3 * 3.
%e 7^2  1 = 48 = 2^4 * 3, so 7 sets the next record, which stands through 11 and 13.
%e 17^2  1 = 288 = 2^5 * 3^2.
%o (PARI) lista(nn) = {r = 0; forprime (n=1, nn, v = valuation(n^21, 2); if (v > r, r = v; print1(n, ", ")));}
%K nonn
%O 1,1
%A _Michel Marcus_, Dec 20 2013
%E a(22)a(28) from _Hiroaki Yamanouchi_, Sep 27 2014
