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

Author

Max Alekseyev and Thomas Ordowski, Apr 20 2017

Keywords

• nonn

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

• 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.

Crossrefs

Cf. A002997, A046145, A285513, A285514.

Programs

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; }