

A084681


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


4



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
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OFFSET

1,3


LINKS

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


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)


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] (* JeanFrançois Alcover, Jul 19 2020 *)


PROG

(PARI) a(n) = if (gcd(10, 9*n) != 1, 0, znorder(Mod(10, 9*n))); \\ Michel Marcus, Feb 23 2019
(GAP) List([1..100], n>OrderMod(10, 9*n)); # Muniru A Asiru, Feb 26 2019


CROSSREFS

Cf. A084680, A190301, A216479.
Sequence in context: A181189 A327889 A221702 * A261038 A285852 A096528
Adjacent sequences: A084678 A084679 A084680 * A084682 A084683 A084684


KEYWORD

nonn


AUTHOR

Lekraj Beedassy, Jun 30 2003


EXTENSIONS

More terms from John W. Layman, Oct 09 2003


STATUS

approved



