A114207 Smallest solution to 10^m == 1 (mod m) having the prime divisor A066364(n).

3, 111, 13203, 20439, 1997001, 22494039, 116226009, 761157, 278522253, 206613747, 17677747557, 835525881, 12933400720959, 228717562653, 5465090439, 13095850041, 431138536893, 4734551277, 58199580096201, 59875330325409, 228520359, 3003003, 257494085001, 1029221499627, 136635497220969

Offset: 1

Author

Max Alekseyev, Nov 17 2005

Keywords

• nonn

Examples

			a(6)=m(5477)=22494039 since it is the smallest m such that 10^m == 1 (mod m) and 5477|m.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..2060 (first 501 terms from Max Alekseyev)

Crossrefs

Cf. A066364.

Programs

PARI

{ m(p) = my(f,l,q); f=factorint(p)[,1]; l=p; for(i=1,length(f),q=znorder(Mod(10,f[i])); l=lcm(l,q); l=lcm(l,m(q)) ); l }

Formula

a(n)=m(p), where p=A066364(n) and m(p)=lcm(p, ord_p(10), m(q)) with q going over all prime divisors of ord_p(10).