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A226785 If n=0 (mod 7) then a(n)=0, otherwise a(n)=7^(-1) in Z/nZ*.

%I A226785 #32 Mar 14 2023 09:21:18
%S A226785 0,1,1,3,3,1,0,7,4,3,8,7,2,0,13,7,5,13,11,3,0,19,10,7,18,15,4,0,25,13,
%T A226785 9,23,19,5,0,31,16,11,28,23,6,0,37,19,13,33,27,7,0,43,22,15,38,31,8,0,
%U A226785 49,25,17,43,35,9,0
%N A226785 If n=0 (mod 7) then a(n)=0, otherwise a(n)=7^(-1) in Z/nZ*.
%H A226785 Charles R Greathouse IV, <a href="/A226785/b226785.txt">Table of n, a(n) for n = 1..10000</a>
%H A226785 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1).
%F A226785 G.f.: -x^2*(x^13 -x^10 -2*x^9 -x^8 -2*x^7 -7*x^6 -x^4 -3*x^3 -3*x^2 -x -1) / (x^14 -2*x^7 +1). a(n) = 2*a(n-7)-a(n-14). - _Colin Barker_, Jun 20 2013
%F A226785 a(7n+1) = 6*n+1, n>0. a(7n+2)=A016777(n). a(7n+3) = A005408(n). a(7n+4) = A016885(n). a(7n+5)= A004767(n). a(7n+6)= n+1. - _R. J. Mathar_, Jun 28 2013
%p A226785 A226785 := proc(n)
%p A226785     local x,a,m ;
%p A226785     a := 7 ;
%p A226785     m := 7 ;
%p A226785     if igcd(n,m) > 1 or n =1 then
%p A226785         0;
%p A226785     else
%p A226785         msolve(x*a=1,n) ;
%p A226785         op(%) ;
%p A226785         op(2,%) ;
%p A226785     end if;
%p A226785 end proc: # _R. J. Mathar_, Jun 28 2013
%t A226785 Inv[a_, mod_] := Which[mod == 1,0, GCD[a, mod] > 1, 0, True, Last@Reduce[a*x == 1, x, Modulus -> mod]];Table[Inv[7, n],{n, 1, 122}]
%t A226785 Join[{0},LinearRecurrence[{0,0,0,0,0,0,2,0,0,0,0,0,0,-1},{1,1,3,3,1,0,7,4,3,8,7,2,0,13},70]] (* _Harvey P. Dale_, Nov 15 2014 *)
%t A226785 Table[If[Mod[n, 7]==0, 0, ModularInverse[7, n]], {n, 1, 100}] (* _Jean-François Alcover_, Mar 14 2023 *)
%o A226785 (PARI) a(n)=if(n%7,lift(Mod(1,n)/7),0) \\ _Charles R Greathouse IV_, Jun 18 2013
%Y A226785 Cf. A092092, A226782-A226787.
%K A226785 nonn,easy
%O A226785 1,4
%A A226785 _José María Grau Ribas_, Jun 18 2013