A131462 Residues of 3^(2^p(n)-1) for Mersenne numbers with prime indices.

0, 3, 3, 3, 992, 3, 3, 3, 877681, 195496587, 3, 36787319437, 1423919640546, 3542630063906, 77319946053101, 6458069995222223, 168313041233693968, 3, 139200566017647400916, 207875641949796659481

Offset: 1

Author

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

Keywords

• nonn

Comments

M_p is prime iff 3 ^ M_p is congruent to 3 mod M_p. Thus M_7 = 127 is prime because 3^127 mod 127 = 3 while M_11 = 2047 is composite because 3^2047 mod 2047 <> 3.

Examples

			a(5) = 3^(2^11-1) mod 2^11-1 = 3^2047 mod 2047 = 992
		

Links

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

Crossrefs

Cf. A095847, A001348, A131458, A131459, A131460, A131461, A131463.

Formula

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