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.

1, 3, 5, 7, 9, 13, 15, 21, 27, 35, 39, 45, 63, 65, 81, 91, 105, 117, 135, 169, 189, 195, 273, 315, 351, 405, 455, 507, 567, 585, 819, 845, 945, 1053, 1183, 1365, 1521, 1701, 1755, 2457, 2535, 2835, 3159, 3549, 4095, 4563, 5265, 5915, 7371, 7605, 8505, 10647

Offset: 1

Author

Arkadiusz Wesolowski, Nov 03 2012

Keywords

• nonn

Comments

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

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

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..74

Crossrefs

Cf. A001220, A077816.

Programs

Mathematica

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

PARI

is(n)=Mod(2,(3837523*n)^2)^eulerphi(3837523*n)==1 \\ Charles R Greathouse IV, Mar 05 2013