A285512 a(n) = smallest integer m>0 such that the positive integers not exceeding m and coprime to n generate the multiplicative group U(Z/nZ).

1, 1, 2, 3, 2, 5, 3, 5, 2, 3, 2, 7, 2, 3, 7, 5, 3, 5, 2, 11, 5, 7, 5, 13, 2, 5, 2, 5, 2, 11, 3, 5, 5, 3, 3, 7, 2, 3, 7, 11, 3, 11, 3, 7, 7, 5, 5, 13, 3, 3, 5, 5, 2, 5, 3, 11, 5, 3, 2, 13, 2, 3, 5, 5, 3, 7, 2, 5, 5, 19, 7, 13, 5, 5

Offset

1,3

Comments

Denoted G(n) in Burthe (1997).

If A046145(n)>0, then a(n) <= A046145(n).

For all n>=3, a(n) is prime.

Links

Table of n, a(n) for n=1..74.

Burthe, R. J., Jr. Upper bounds for least witnesses and generating sets. Acta Arith. 80:4 (1997), 311-326.

Wikipedia, Multiplicative group of integers modulo n.

Prog

(PARI) { A285512(n) = my(S, s, t); S=Set([Mod(1, n)]); t=1; while( #S!=eulerphi(n), until(n%t, t=nextprime(t+1)); until(#S==s, s=#S; S=setunion(S, Set(S*t))); ); t; }

Crossrefs

Cf. A002997, A046145, A285513, A285514.

Sequence in context: A131470 A352708 A255709 * A232928 A323021 A026235

Adjacent sequences: A285509 A285510 A285511 * A285513 A285514 A285515

Keyword

nonn

Author

Max Alekseyev and Thomas Ordowski, Apr 20 2017

Status

approved