%I
%S 1,9,5,7,6,3,8,4,2,1,9,5,7,6,3,8,4,2,1,9,5,7,6,3,8,4,2,
%T 1,9,5,7,6,3,8,4,2,1,9,5,7,6,3,8,4,2,1,9,5,7,6,3,8,4,2,1,
%U 9,5,7,6,3,8,4,2,1,9,5,7,6,3,8,4,2
%N A variation on 10^n mod 19
%C This sequence can be employed in a test for divisibility by 19 and works like A033940 works for 7.
%C The use of negative coefficients ensures the termination of the test because the modulus of the intermediate sum at each step of the test decreases strictly.
%C The test is successful if the final sum is 0.
%C The negative coefficients have the form (10^n mod 19)  19 when 10^n mod 19 > 9.
%C Example: 8284 is divisible by 19 since 4*1 + 8*(9) + 2*5 + 8*(7) = 114 and 4*1 + 1*(9) + 1*5 = 0.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).
%F a(n) = a(n9). G.f.: (2*x^84*x^78*x^6+3*x^5+6*x^47*x^3+5*x^29*x+1) / (x^9+1). [_Colin Barker_, Feb 14 2013]
%Y Cf. A033940, A119910, A117378.
%K easy,sign
%O 0,2
%A Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 26 2009
