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

1,2

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.

Links

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

Formula

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

Example

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

Crossrefs

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

Sequence in context: A184181 A020003 A276750 * A326341 A062794 A036235

Adjacent sequences: A131457 A131458 A131459 * A131461 A131462 A131463

Keyword

nonn

Author

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

Status

approved