A084681 Order of 10 modulo 9n [i.e., least m such that 10^m = 1 (mod 9n)] or 0 when no such number exists.

1, 0, 3, 0, 0, 0, 6, 0, 9, 0, 2, 0, 6, 0, 0, 0, 16, 0, 18, 0, 6, 0, 22, 0, 0, 0, 27, 0, 28, 0, 15, 0, 6, 0, 0, 0, 3, 0, 6, 0, 5, 0, 21, 0, 0, 0, 46, 0, 42, 0, 48, 0, 13, 0, 0, 0, 18, 0, 58, 0, 60, 0, 18, 0, 0, 0, 33, 0, 66, 0, 35, 0, 8, 0, 0, 0, 6, 0, 13, 0, 81, 0, 41, 0, 0, 0, 84, 0, 44, 0, 6, 0, 15, 0

Offset: 1

Author

Lekraj Beedassy, Jun 30 2003

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• K. Matthews, Finding the order of a (mod m)

Crossrefs

Cf. A084680, A190301, A216479.

Programs

GAP

List([1..100],n->OrderMod(10,9*n)); # Muniru A Asiru, Feb 26 2019

Maple

f:= proc(n)
if igcd(n,10)>1 then 0 else numtheory:-order(10,9*n) fi
end proc:
map(f, [$1..100]); # Robert Israel, Feb 22 2019

Mathematica

a[n_] := If[GCD[10, 9n] != 1, 0, MultiplicativeOrder[10, 9n]];
Array[a, 100] (* Jean-François Alcover, Jul 19 2020 *)

PARI

a(n) = if (gcd(10, 9*n) != 1, 0, znorder(Mod(10, 9*n))); \\ Michel Marcus, Feb 23 2019

Formula

From Robert Israel, Feb 22 2019: (Start)

a(n) = A084680(9*n).

If n is not divisible by 3, a(n) = A084680(n).

Otherwise a(n) can be either A084680(n), 3*A084680(n) or 9*A084680(n). (End)

Extensions

More terms from John W. Layman, Oct 09 2003