A248755 a(n) is the number of iterations for the Lucas-Lehmer sequence A003010 (mod p_n) to enter a loop, where p_n is the n-th prime number A000040(n).

2, 2, 1, 4, 3, 3, 4, 2, 5, 4, 6, 5, 4, 5, 11, 3, 15, 6, 5, 3, 5, 6, 11, 13, 5, 4, 9, 27, 11, 10, 8, 7, 23, 13, 20, 12, 14, 10, 41, 28, 12, 4, 36, 4, 15, 13, 27, 8, 15, 11, 13, 24, 5, 51, 8, 65, 36, 8, 13, 47, 36, 42, 31, 20, 13, 52, 42, 6, 87, 16, 30, 89, 15, 7, 36, 95, 6, 17, 34, 10

Offset: 1

Author

Robert G. Wilson v, Oct 13 2014

Keywords

• nonn
• easy

Comments

The Lucas-Lehmer sequence is used to test for Mersenne primes (A001348), but this is irrelevant for this sequence.

Examples

			a(4) is 4 because p_4 = 7, and the sequence A003010 (mod 7) becomes -> 4, 0, 5, 2, 2, 2, 2, 2, 2, .... The term 2 which is the first term of an infinite loop is at position 4.
		

Links

• GIMPS, Great Internet Mersenne Prime Search
• Eric W. Weisstein's World of Mathematics, Lucas-Lehmer Test
• Wikipedia, Lucas-Lehmer primality test

Crossrefs

Cf. A003010, A001348, A095847, A000043.

Programs

Mathematica

f[n_] := -1 + Length@ NestWhileList[ Mod[#^2 - 2, Prime[n]] &, 4, UnsameQ[##] &, {2, Infinity}]; Array[f, 80]