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

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)) 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.

Examples

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

Links

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

Crossrefs

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

Formula

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