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

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 (-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.

Examples

			a(5) = 3^(2^(11-1)-1) Mod 2^11-1 = 3^1023 Mod 2047 = 1565
		

Links

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

Crossrefs

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

Formula

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