A055685 Numbers k such that 2^k == -1 (mod k-1).

2, 6, 66, 378, 1190, 1470, 25806, 58590, 134946, 137346, 170586, 272610, 285390, 420210, 538734, 592410, 618450, 680706, 778806, 1163066, 1520442, 1700946, 2099202, 2831010, 4020030, 4174170, 4516110, 5059890, 5215770

Offset: 1

Author

Robert G. Wilson v, Jun 09 2000

Keywords

• nonn

Comments

The sequence is infinite. In fact, even its intersection with A006517 (given by A219037) is infinite.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1192
• Kin Y. Li et al., Solution to Problem 323, Mathematical Excalibur 14(2), 2009, p. 3.

Crossrefs

Cf. A064935, A006517, A219037, A296369.

Programs

Mathematica

Do[If[PowerMod[2, n, n-1]==n-2, Print[n]], {n, 2, 12900000}]

Python

A055685_list = [n for n in range(2,10**6) if pow(2,n,n-1) == n-2] # Chai Wah Wu, Nov 04 2019

Formula

a(n) = A296369(n) + 1.

Extensions

Edited by Max Alekseyev, Oct 11 2012

Incorrect term 4285390 removed by Chai Wah Wu, Nov 04 2019