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

1,1

Comments

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

Links

Table of n, a(n) for n=1..80.

GIMPS, Great Internet Mersenne Prime Search

Eric W. Weisstein's World of Mathematics, Lucas-Lehmer Test

Wikipedia, Lucas-Lehmer primality test

Example

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.

Mathematica

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

Crossrefs

Cf. A003010, A001348, A095847, A000043.

Sequence in context: A122918 A177424 A286332 * A129903 A263203 A023616

Adjacent sequences: A248752 A248753 A248754 * A248756 A248757 A248758

Keyword

nonn,easy

Author

Robert G. Wilson v, Oct 13 2014

Status

approved