A354269 Numbers b such that b^(11-1) == 1 (mod 11^2) and b^(1006003-1) == 1 (mod 1006003^2), i.e., common Wieferich bases of 11 and 1006003.

1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 31098449, 34970654, 35236643, 43046721, 58883189, 73220005, 93295347, 102199060, 104911962, 105709929, 112028791, 112870007, 115196746, 117560414, 129140163, 144185176

Offset

1,2

Comments

A000244 is a subsequence.

Links

Table of n, a(n) for n=1..32.

Prog

(PARI) is(n) = my(p=11, q=1006003); Mod(n, p^2)^(p-1)==1 && Mod(n, q^2)^(q-1)==1
(Python)
def ok(b): return pow(b, 10, 121)==1 and pow(b, 1006002, 1006003**2)==1
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, May 25 2022

Crossrefs

Cf. A000244, A014127, A247208.

Sequence in context: A190128 A216097 A243845 * A140429 A141413 A000244

Adjacent sequences: A354266 A354267 A354268 * A354270 A354271 A354272

Keyword

nonn

Author

Felix Fröhlich, May 25 2022

Status

approved