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

1,7

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

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 *)

Prog

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

Crossrefs

Cf. A007732, A002329, A070682, A216415.

Sequence in context: A137378 A333275 A293071 * A051626 A357003 A264808

Adjacent sequences: A084677 A084678 A084679 * A084681 A084682 A084683

Keyword

nonn

Author

Lekraj Beedassy, Jun 30 2003

Extensions

More terms from John W. Layman, Aug 12 2003

Status

approved