A084680 Order of 10 modulo n [i.e., least m such that 10^m = 1 (mod n)] or 0 when no such number exists.

1, 0, 1, 0, 0, 0, 6, 0, 1, 0, 2, 0, 6, 0, 0, 0, 16, 0, 18, 0, 6, 0, 22, 0, 0, 0, 3, 0, 28, 0, 15, 0, 2, 0, 0, 0, 3, 0, 6, 0, 5, 0, 21, 0, 0, 0, 46, 0, 42, 0, 16, 0, 13, 0, 0, 0, 18, 0, 58, 0, 60, 0, 6, 0, 0, 0, 33, 0, 22, 0, 35, 0, 8, 0, 0, 0, 6, 0, 13, 0, 9, 0, 41, 0, 0, 0, 28, 0, 44, 0, 6, 0, 15, 0, 0, 0

Offset: 1

Author

Lekraj Beedassy, Jun 30 2003

Keywords

• nonn

Comments

When n is not divisible by 2 or 5, a(n) = A007732(n). A002329 contains the nonzero terms.

A number k > 0 appears in this sequence exactly A059892(k) times. - T. D. Noe, May 18 2007

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A007732, A002329, A070682, A216415.

Programs

GAP

List([1..100],n->OrderMod(10,n)); # Muniru A Asiru, Feb 26 2019

Maple

A084680 := proc(n) if gcd(n,10) <> 1 then 0 ; elif n = 1 then 1 ; else numtheory[order](10,n) ; end if; end proc: seq(A084680(n),n=2..100) ; # R. J. Mathar, Mar 10 2010

Mathematica

a[n_] := If[!CoprimeQ[n, 10], 0, MultiplicativeOrder[10, n]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Nov 07 2012 *)

PARI

a(n,b=10)=if(gcd(n,b)!=1,0,znorder(Mod(b,n)));
vector(66,n,a(n)) \\ Joerg Arndt, Nov 15 2014

Extensions

More terms from John W. Layman, Aug 12 2003