A218584 - OEIS

A218584

Numbers n such that 2^A000010(n*x) == 1 (mod (n*x)^2), where x = 3837523 is the product of the first 2 Wieferich primes 1093 and 3511.

%I #11 Mar 05 2013 00:51:27

%S 1,3,5,7,9,13,15,21,27,35,39,45,63,65,81,91,105,117,135,169,189,195,

%T 273,315,351,405,455,507,567,585,819,845,945,1053,1183,1365,1521,1701,

%U 1755,2457,2535,2835,3159,3549,4095,4563,5265,5915,7371,7605,8505,10647

%N Numbers n such that 2^A000010(n*x) == 1 (mod (n*x)^2), where x = 3837523 is the product of the first 2 Wieferich primes 1093 and 3511.

%C 3837523*a(n) is a term in A077816.

%C If this sequence is finite, then there are finitely many Wieferich primes (A001220).

%H Arkadiusz Wesolowski, <a href="/A218584/b218584.txt">Table of n, a(n) for n = 1..74</a>

%t x = 3837523; Select[Range[1, 10647, 2], PowerMod[2, EulerPhi[#*x], (#*x)^2] == 1 &]

%o (PARI) is(n)=Mod(2,(3837523*n)^2)^eulerphi(3837523*n)==1 \\ _Charles R Greathouse IV_, Mar 05 2013

%Y Cf. A001220, A077816.

%K nonn

%O 1,2

%A _Arkadiusz Wesolowski_, Nov 03 2012