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A233930
Primes p that give record exponents of 2 in p^2 - 1 (A091282).
2
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
1,1
COMMENTS
Among these terms, we find the first Mersenne primes (A000668), and some Fermat numbers (A000215).
LINKS
EXAMPLE
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.
PROG
(PARI) lista(nn) = {r = 0; forprime (n=1, nn, v = valuation(n^2-1, 2); if (v > r, r = v; print1(n, ", "))); }
CROSSREFS
Sequence in context: A099983 A275631 A048860 * A292447 A176690 A295089
KEYWORD
nonn
AUTHOR
Michel Marcus, Dec 20 2013
EXTENSIONS
a(22)-a(28) from Hiroaki Yamanouchi, Sep 27 2014
STATUS
approved