Search: id:A155751
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%I A155751
%S A155751 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 A155751 4,6,8,5,1,7,2,3,4,6,8,5,1,7,2,3,4,6,8,5,1,7,2,3,4,6,8,5,
%U A155751 1,7,2,3,4,6,8,5,1,7,2,3,4,6,8,5,1,7,2,3,4,6,8,5
%V A155751 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,
%W A155751 -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,
               5,
%X A155751 -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 A155751 A variation on 10^n mod 17
%C A155751 This sequence can be employed in a test for divisibility by 17 and works 
               like A033940 works for 7.
%C A155751 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 stricly.
%C A155751 The test is successful if the final sum is 0.
%C A155751 The negative coefficients have the form (10^n mod 17) - 17 when 10^n 
               mod 17 > 8.
%C A155751 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 A155751 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 (mathar(AT)strw.leidenuniv.nl), Feb 13 2009]
%Y A155751 Cf. A033940, A119910, A117378.
%Y A155751 Sequence in context: A021857 A163333 A116369 this_sequence A092234 A160101 
               A065476
%Y A155751 Adjacent sequences: A155748 A155749 A155750 this_sequence A155752 A155753 
               A155754
%K A155751 easy,sign,uned
%O A155751 0,2
%A A155751 Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 26 2009, Feb 08 2009
%E A155751 How is the sequence defined? - N. J. A. Sloane (njas(AT)research.att.com), 
               Feb 08 2009

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