A131459 Residues of 3^(2^(p(n)-1)) for Mersenne numbers with prime indices.

0, 4, 28, 124, 601, 8188, 131068, 524284, 5758678, 269332797, 2147483644, 60499757946, 322343434415, 5567835897839, 16557488261208, 7853427629182494, 426047939903614778, 2305843009213693948, 141920345591572240917

Offset

1,2

Comments

Mp is prime iff 3^(2^(p(n)-1)) is congruent to (-3) Mod Mp. Thus M7 = 127 is prime because 3^64 Mod 127 = 124 (=127-3) while M11 = 2047 is composite because 3^1024 Mod 2047 <> 2044.

Links

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

Formula

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

Example

a(5) = 3^(2^(11-1)) Mod 2^11-1 = 3^1024 Mod 2047 = 601

Crossrefs

Cf. A095847, A001348, A131458, A131460, A131461, A131462, A131463.

Sequence in context: A212900 A196514 A249629 * A231581 A223115 A296381

Adjacent sequences: A131456 A131457 A131458 * A131460 A131461 A131462

Keyword

nonn

Author

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

Status

approved