A267288 Composites c where at least one base b with 1 < b < c exists such that b^(c-1) == 1 (mod c^2), i.e., composites c that are base-b 'Wieferich pseudoprimes' for at least one b between 1 and c.

133, 451, 561, 871, 904, 1065, 1105, 1267, 1729, 1891, 2059, 2201, 2501, 2821, 2993, 3145, 4641, 5005, 5551, 5841, 5963, 6409, 6541, 6601, 6697, 7107, 7471, 7501, 8321, 8323, 9637, 10585, 11266, 12209, 12403, 13571, 13585, 16471, 17261, 17466, 17770, 18103

Offset

1,1

Comments

A002808(i) such that A256517(i) < A002808(i).

Any term is also a term of A039769.

Links

Amiram Eldar, Table of n, a(n) for n = 1..350

Example

871 is a term of the sequence, since 699^870 == 1 (mod 871^2) and 699 < 871.

Mathematica

q[c_] := CompositeQ[c] && AnyTrue[Range[2, c-1], PowerMod[#, c-1, c^2] == 1 &]; Select[Range[5000], q] (* Amiram Eldar, Jan 23 2026 *)

Prog

(PARI) forcomposite(c=2, , for(b=2, c-1, if(Mod(b, c^2)^(c-1)==1, print1(c, ", "); break({1}))))

Crossrefs

Cf. A002808, A039769, A134307, A255885, A256517.

Sequence in context: A070158 A055940 A251131 * A334037 A137879 A249108

Adjacent sequences: A267285 A267286 A267287 * A267289 A267290 A267291

Keyword

nonn

Author

Felix Fröhlich, Jan 12 2016

Status

approved