A131461 Residues of 3^(2^p(n)-2) for Mersenne numbers with prime indices.

0, 1, 1, 1, 1013, 1, 1, 1, 5884965, 65165529, 1, 103888408793, 474639880182, 4112907695371, 72685811469476, 5155089749987738, 440411515280180314, 1, 95591506202441271281, 69291880649932219827

Offset: 1

Author

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

Keywords

• nonn

Comments

M_p is prime iff 3^(M_p-1) is congruent to 1 mod M_p. Thus M_7 = 127 is prime because 3^126 mod 127 = 1 while M_11 = 2047 is composite because 3^2046 mod 2047 <> 1.

Examples

			a(5) = 3^(2^11-2) mod 2^11-1 = 3^2046 mod 2047 = 1013
		

Links

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

Crossrefs

Cf. A095847, A001348, A131458, A131459, A131460, A131462, A131463.

Formula

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