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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Among these terms, we find the first Mersenne primes (A000668), and some Fermat numbers (A000215). LINKS Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100 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 Adjacent sequences:  A233927 A233928 A233929 * A233931 A233932 A233933 KEYWORD nonn AUTHOR Michel Marcus, Dec 20 2013 EXTENSIONS a(22)-a(28) from Hiroaki Yamanouchi, Sep 27 2014 STATUS approved

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Last modified September 16 06:38 EDT 2019. Contains 327090 sequences. (Running on oeis4.)