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

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

%S 0,2,9,9,929,9,9,9,2633043,49618850,9,110361958311,2072735666087,

%T 1831797169511,91222349803976,1359811476184687,504939123701081904,9,

%U 122453792873589376894,623626925849389978443

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

%C M_p is prime iff 3^(M_p+1) is congruent to 9 mod M_p. Thus M_7 = 127 is prime because 3^128 mod 127 = 9 while M_11 = 2047 is composite because 3^2048 mod 2047 <> 9.

%H Dennis Martin, <a href="/A131463/b131463.txt">Table of n, a(n) for n = 1..100</a>

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

%e a(5) = 3^(2^11) mod 2^11-1 = 3^2048 mod 2047 = 929

%Y Cf. A095847, A001348, A131458, A131459, A131460, A131461, A131462.

%K nonn

%O 1,2

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