

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).


6



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
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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), 311326.
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: A162398 A131470 A255709 * A232928 A026235 A086281
Adjacent sequences: A285509 A285510 A285511 * A285513 A285514 A285515


KEYWORD

nonn


AUTHOR

Max Alekseyev and Thomas Ordowski, Apr 20 2017


STATUS

approved



