A055685 - OEIS

%I #23 Jul 11 2021 20:15:42

%S 2,6,66,378,1190,1470,25806,58590,134946,137346,170586,272610,285390,

%T 420210,538734,592410,618450,680706,778806,1163066,1520442,1700946,

%U 2099202,2831010,4020030,4174170,4516110,5059890,5215770

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

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

%H Chai Wah Wu, <a href="/A055685/b055685.txt">Table of n, a(n) for n = 1..1192</a>

%H Kin Y. Li et al., <a href="http://www.math.ust.hk/excalibur/v14_n2.pdf">Solution to Problem 323</a>, Mathematical Excalibur 14(2), 2009, p. 3.

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

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

%o (Python)

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

%Y Cf. A064935, A006517, A219037, A296369.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jun 09 2000

%E Edited by _Max Alekseyev_, Oct 11 2012

%E Incorrect term 4285390 removed by _Chai Wah Wu_, Nov 04 2019