A233930 Primes p that give record exponents of 2 in p^2 - 1 (A091282).

3, 7, 17, 31, 127, 257, 3583, 5119, 6143, 8191, 65537, 131071, 524287, 7340033, 14680063, 104857601, 109051903, 167772161, 469762049, 2013265921, 2147483647, 21474836479, 51539607551, 206158430209, 824633720831, 2748779069441, 6597069766657, 26388279066623

Offset: 1

Author

Michel Marcus, Dec 20 2013

Keywords

• nonn

Comments

Among these terms, we find the first Mersenne primes (A000668), and some Fermat numbers (A000215).

Examples

			3^2 - 1 = 8 = 2^3. 5 does not beat this record with 5^2 - 1 = 24 = 2^3 * 3.
7^2 - 1 = 48 = 2^4 * 3, so 7 sets the next record, which stands through 11 and 13.
17^2 - 1 = 288 = 2^5 * 3^2.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100

Programs

PARI

lista(nn) = {r = 0; forprime (n=1, nn, v = valuation(n^2-1, 2); if (v > r, r = v; print1(n, ", ")));}

Extensions

a(22)-a(28) from Hiroaki Yamanouchi, Sep 27 2014