A131463 Residues of 3^(2^p(n)) for Mersenne numbers with prime indices.

0, 2, 9, 9, 929, 9, 9, 9, 2633043, 49618850, 9, 110361958311, 2072735666087, 1831797169511, 91222349803976, 1359811476184687, 504939123701081904, 9, 122453792873589376894, 623626925849389978443

Offset: 1

Author

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

Keywords

• nonn

Comments

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.

Examples

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

Links

• Dennis Martin, Table of n, a(n) for n = 1..100

Crossrefs

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

Formula

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