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%I #12 Oct 19 2017 10:46:17
%S 1,-7,-2,-3,4,6,-8,5,-1,7,2,3,-4,-6,8,-5,1,-7,-2,-3,4,6,-8,5,-1,7,2,3,
%T -4,-6,8,-5,1,-7,-2,-3,4,6,-8,5,-1,7,2,3,-4,-6,8,-5,1,-7,-2,-3,4,6,-8,
%U 5,-1,7,2,3,-4,-6,8,-5,1,-7,-2,-3,4,6,-8,5,-1,7,2,3,-4,-6,8,-5
%N A variation on 10^n mod 17
%C This is 10^n mod 17, using values -8,-7,...,7,8 (instead of 0..16). - _Don Reble_, Sep 02 2017.
%C This sequence can be employed in a test for divisibility by 17 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 17) - 17 when 10^n mod 17 > 8.
%C Example: 9996 is divisible by 17 since |6*1 + 9*(-7) + 9*(-2) + 9*(-3)| = 102 and 2*1 + 0*(-7) + 1*(-2) = 0.
%F a(n)= -a(n-8). G.f.:(1-7x-2x^2-3x^3+4x^4+6x^5-8x^6+5x^7)/(1+x^8). [From _R. J. Mathar_, Feb 13 2009]
%Y Cf. A033940, A119910, A117378.
%K easy,sign
%O 0,2
%A Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 26 2009, Feb 08 2009
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