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A226783 If n=0 (mod 5) then a(n)=0, otherwise a(n)=5^(-1) in Z/nZ*.

%I A226783 #26 Mar 14 2023 09:21:09
%S A226783 0,1,2,1,0,5,3,5,2,0,9,5,8,3,0,13,7,11,4,0,17,9,14,5,0,21,11,17,6,0,
%T A226783 25,13,20,7,0,29,15,23,8,0,33,17,26,9,0,37,19,29,10,0,41,21,32,11,0,
%U A226783 45,23,35,12,0,49,25,38
%N A226783 If n=0 (mod 5) then a(n)=0, otherwise a(n)=5^(-1) in Z/nZ*.
%H A226783 Charles R Greathouse IV, <a href="/A226783/b226783.txt">Table of n, a(n) for n = 1..10000</a>
%H A226783 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,0,-1).
%F A226783 G.f.: -x^2*(x^9-x^6-x^5-5*x^4-x^2-2*x-1) / ( (x-1)^2*(x^4+x^3+x^2+x+1)^2 ). - _Colin Barker_, Jun 20 2013
%F A226783 a(5n+1) = A016813(n), n>0. a(5n+2)= A005408(n), n>0. a(5n+3) = A016789(n). a(5n+4)=n+1. - _R. J. Mathar_, Jun 28 2013
%F A226783 a(n) = Sum_{k=1..n} k*(floor((5k-1)/n)-floor((5k-2)/n)), n>1. - _Anthony Browne_, Jun 19 2016
%p A226783 A226783 := proc(n)
%p A226783     local x ;
%p A226783     a := 5 ;
%p A226783     m := 5 ;
%p A226783     if n mod m = 0 or n = 1 then
%p A226783         0;
%p A226783     else
%p A226783         msolve(x*a=1,n) ;
%p A226783         op(%) ;
%p A226783         op(2,%) ;
%p A226783     end if;
%p A226783 end proc: # _R. J. Mathar_, Jun 28 2013
%t A226783 Inv[a_, mod_] := Which[mod == 1,0, GCD[a, mod] > 1, 0, True, Last@Reduce[a*x == 1, x, Modulus -> mod]];Table[Inv[5, n], {n, 1, 122}]
%t A226783 CoefficientList[Series[-x^2(x^9-x^6-x^5-5x^4-x^2-2x-1)/((x-1)^2 (x^4+ x^3+ x^2+ x+ 1)^2),{x,0,120}],x] (* _Harvey P. Dale_, Oct 08 2016 *)
%t A226783 Table[If[Mod[n, 5]==0, 0, ModularInverse[5, n]], {n, 1, 100}] (* _Jean-François Alcover_, Mar 14 2023 *)
%o A226783 (PARI) a(n)=if(n%5,lift(Mod(1, n)/5),0) \\ _Charles R Greathouse IV_, Jun 18 2013
%Y A226783 Cf. A092092, A226782-A226787.
%K A226783 nonn,easy
%O A226783 1,3
%A A226783 _José María Grau Ribas_, Jun 18 2013