A084680 - OEIS

%I #32 Feb 26 2019 03:45:24

%S 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,

%T 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,

%U 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

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

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

%C A number k > 0 appears in this sequence exactly A059892(k) times. - _T. D. Noe_, May 18 2007

%H T. D. Noe, <a href="/A084680/b084680.txt">Table of n, a(n) for n=1..1000</a>

%p 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

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

%o (PARI) a(n,b=10)=if(gcd(n,b)!=1,0,znorder(Mod(b,n)));

%o vector(66,n,a(n)) \\ _Joerg Arndt_, Nov 15 2014

%o (GAP) List([1..100],n->OrderMod(10,n)); # _Muniru A Asiru_, Feb 26 2019

%Y Cf. A007732, A002329, A070682, A216415.

%K nonn

%O 1,7

%A _Lekraj Beedassy_, Jun 30 2003

%E More terms from _John W. Layman_, Aug 12 2003