A158248 Composite numbers with primitive root 10.

49, 289, 343, 361, 529, 841, 2209, 2401, 3481, 3721, 4913, 6859, 9409, 11881, 12167, 12769, 16807, 17161, 22201, 24389, 27889, 32041, 32761, 37249, 49729, 52441, 54289, 66049, 69169, 72361, 83521, 97969

Offset: 1

Author

Robert Hutchins, Mar 15 2009

Keywords

• nonn
• base

Comments

Previous name was: Numbers m whose reciprocal generates a repeating decimal fraction with period phi(m) and m/2 < phi(m) < m-1.

All terms are proper powers of full reptend primes (A001913).

This sequence does not contain every proper power of every term in A001913, for example, A001913 has 487 as its 26th term, but since 10 is not a primitive root of 487^2, 487^2 is not a term of this sequence. - Robert Hutchins, Oct 14 2021

A shorter description appears to be "Composite numbers with primitive root 10". - Arkadiusz Wesolowski, Jul 04 2012 (The two definitions certainly produce the same terms up through 83521. - N. J. A. Sloane, Jul 05 2012)

Links

• Ray Chandler, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007732, A001913, A046145, A046146.

Subsequence of A244623.

Subsequence of A167797.

Cf. A108989 (for base 2), A346316 (for base 6).

Programs

Maple

select(n -> not isprime(n) and numtheory:-primroot(9,n) = 10,[$2..10000]);
# N. J. A. Sloane, Jul 05 2012

Mathematica

Select[Range[10^5], GCD[10, #] == 1 && #/2 < MultiplicativeOrder[10, #] < # - 1 &] (* Ray Chandler, Oct 17 2012 *)

Extensions

More terms from Robert Hutchins, Mar 21 2009

Entry revised by N. J. A. Sloane, Jul 05 2012

New name (using comment by Arkadiusz Wesolowski) from Joerg Arndt, Nov 22 2021