login
Residues of 3^(2^(p(n)-1)-1) for Mersenne numbers with prime indices.
6

%I #3 Nov 11 2010 07:34:06

%S 0,6,30,126,1565,8190,131070,524286,7511964,89777599,2147483646,

%T 20166585982,840455563322,4787976306682,5519162753736,

%U 2617809209727498,334169564069012755,2305843009213693950,47306781863857413639

%N Residues of 3^(2^(p(n)-1)-1) for Mersenne numbers with prime indices.

%C Mp is prime iff 3^(2^(p(n)-1)-1) is congruent to (-1) Mod Mp. Thus M7 = 127 is prime because 3^63 Mod 127 = 126 (=127-1) while M11 = 2047 is composite because 3^1023 Mod 2047 <> 2046.

%H Dennis Martin, <a href="/A131458/b131458.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = 3^(2^(p(n)-1)-1) Mod 2^p(n)-1

%e a(5) = 3^(2^(11-1)-1) Mod 2^11-1 = 3^1023 Mod 2047 = 1565

%Y Cf. A095847, A001348, A131459, A131460, A131461, A131462, A131463.

%K nonn

%O 1,2

%A Dennis Martin (dennis.martin(AT)dptechnology.com), Jul 13 2007, Jul 20 2007