A131458 Residues of 3^(2^(p(n)-1)-1) for Mersenne numbers with prime indices.

0, 6, 30, 126, 1565, 8190, 131070, 524286, 7511964, 89777599, 2147483646, 20166585982, 840455563322, 4787976306682, 5519162753736, 2617809209727498, 334169564069012755, 2305843009213693950, 47306781863857413639

Offset

1,2

Comments

Mp is prime iff 3^(2^(p(n)-1)-1) is congruent to (-1) Mod Mp. Thus M7 = 127 is prime because 3^63 Mod 127 = 126 (=127-1) while M11 = 2047 is composite because 3^1023 Mod 2047 <> 2046.

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 = 3^1023 Mod 2047 = 1565

Crossrefs

Cf. A095847, A001348, A131459, A131460, A131461, A131462, A131463.

Sequence in context: A174319 A337456 A334326 * A032205 A007465 A261389

Adjacent sequences: A131455 A131456 A131457 * A131459 A131460 A131461

Keyword

nonn

Author

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

Status

approved