A231372 Squarefree composite numbers k such that 10 is a primitive root for all prime factors of k.

119, 133, 161, 203, 323, 329, 391, 413, 427, 437, 493, 551, 667, 679, 763, 791, 799, 893, 917, 1003, 1037, 1043, 1081, 1121, 1159, 1169, 1253, 1267, 1351, 1357, 1363, 1403, 1561, 1603, 1631, 1649, 1711, 1769, 1799, 1841, 1843, 1853, 1883, 1921, 2071, 2147, 2191

Offset

1,1

Comments

If k is the smallest integer satisfying 10^k == 1 (mod p), we say that 10 has order k (mod p). If n is the product of distinct primes p_i, the period of 1/n in base b is the least common multiple of the orders of b (mod p_i), provided b and n are relatively prime.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Primitive Root.

Wikipedia, Decimal.

Mathematica

q[n_] := CompositeQ[n] && SquareFreeQ[n] && AllTrue[FactorInteger[n][[;; , 1]],  MultiplicativeOrder[10, #] == # - 1 &]; Select[Range[2000], q] (* Amiram Eldar, Oct 03 2021 *)

Crossrefs

Subsequence of A024556.

Cf. A001913, A231370, A231371.

Sequence in context: A328973 A133626 A124074 * A103154 A039557 A095629

Adjacent sequences: A231369 A231370 A231371 * A231373 A231374 A231375

Keyword

nonn

Author

Arkadiusz Wesolowski, Nov 08 2013

Status

approved