A131460 Residues of 3^(2^(p(n)-1)+1) for Mersenne numbers with prime indices.

0, 5, 22, 118, 1803, 8182, 131062, 524278, 498820, 271127480, 2147483638, 44060320367, 967030303245, 7907414671310, 49672464783624, 5545884378065500, 125222315103997360, 2305843009213693942, 130613131595363896897

Offset: 1

Author

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

Keywords

• nonn

Comments

Mp is prime iff 3^(2^(p(n)-1)+1) is congruent to (-9) Mod Mp. Thus M7 = 127 is prime because 3^65 Mod 127 = 118 (=127-9) while M11 = 2047 is composite because 3^1025 Mod 2047 <> 2038.

Examples

			a(5) = 3^(2^(11-1)+1) Mod 2^11-1 = 3^1025 Mod 2047 = 1803
		

Links

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

Crossrefs

Cf. A095847, A001348, A131458, A131459, A131461, A131462, A131463.

Formula

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