1,1

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.

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

Eric Weisstein's World of Mathematics, Primitive Root.

Wikipedia, Binary number.

q[n_] := CompositeQ[n] && SquareFreeQ[n] && AllTrue[FactorInteger[n][[;; , 1]], MultiplicativeOrder[2, #] == # - 1 &]; Select[Range[700], q] (* Amiram Eldar, Oct 03 2021 *)

(PARI) isok(k) = if ((k>1) && (k%2) && !isprime(k) && issquarefree(k), my(f=factor(k)[, 1]~); for (j=1, #f, if (znorder(Mod(2, f[j])) != (f[j]-1), return(0))); return (1)); return (0); \\ Michel Marcus, Oct 03 2021

Subsequence of A024556.

Cf. A001122, A231371, A231372.

Sequence in context: A140608 A085371 A162887 * A246755 A212311 A262741

Adjacent sequences: A231367 A231368 A231369 * A231371 A231372 A231373

Arkadiusz Wesolowski, Nov 08 2013

approved