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

%I A084681 #30 Nov 29 2020 01:03:03
%S A084681 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,
%T A084681 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,
%U A084681 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
%N A084681 Order of 10 modulo 9n [i.e., least m such that 10^m = 1 (mod 9n)] or 0 when no such number exists.
%H A084681 Robert Israel, <a href="/A084681/b084681.txt">Table of n, a(n) for n = 1..10000</a>
%H A084681 K. Matthews, <a href="http://www.numbertheory.org/php/order.html">Finding the order of a (mod m)</a>
%F A084681 From _Robert Israel_, Feb 22 2019: (Start)
%F A084681 a(n) = A084680(9*n).
%F A084681 If n is not divisible by 3, a(n) = A084680(n).
%F A084681 Otherwise a(n) can be either A084680(n), 3*A084680(n) or 9*A084680(n). (End)
%p A084681 f:= proc(n)
%p A084681 if igcd(n,10)>1 then 0 else numtheory:-order(10,9*n) fi
%p A084681 end proc:
%p A084681 map(f, [$1..100]); # _Robert Israel_, Feb 22 2019
%t A084681 a[n_] := If[GCD[10, 9n] != 1, 0, MultiplicativeOrder[10, 9n]];
%t A084681 Array[a, 100] (* _Jean-François Alcover_, Jul 19 2020 *)
%o A084681 (PARI) a(n) = if (gcd(10, 9*n) != 1, 0, znorder(Mod(10, 9*n))); \\ _Michel Marcus_, Feb 23 2019
%o A084681 (GAP) List([1..100],n->OrderMod(10,9*n)); # _Muniru A Asiru_, Feb 26 2019
%Y A084681 Cf. A084680, A190301, A216479.
%K A084681 nonn
%O A084681 1,3
%A A084681 _Lekraj Beedassy_, Jun 30 2003
%E A084681 More terms from _John W. Layman_, Oct 09 2003