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 A155754 A variation on 10^n mod 19 0
 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, 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, -9, 5, -7, 6, 3, -8, -4, -2, -1, 9, -5, 7, -6, -3, 8, 4, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence can be employed in a test for divisibility by 19 and works like A033940 works for 7. 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. The test is successful if the final sum is 0. The negative coefficients have the form (10^n mod 19) - 19 when 10^n mod 19 > 9. Example: 8284 is divisible by 19 since |4*1 + 8*(-9) + 2*5 + 8*(-7)| = 114 and 4*1 + 1*(-9) + 1*5 = 0. LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,-1). FORMULA a(n) = -a(n-9). G.f.: (-2*x^8-4*x^7-8*x^6+3*x^5+6*x^4-7*x^3+5*x^2-9*x+1) / (x^9+1). [Colin Barker, Feb 14 2013] CROSSREFS Cf. A033940, A119910, A117378. Sequence in context: A292824 A021515 A011259 * A273840 A117019 A155692 Adjacent sequences:  A155751 A155752 A155753 * A155755 A155756 A155757 KEYWORD easy,sign AUTHOR Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 26 2009 STATUS approved

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Last modified December 16 07:12 EST 2018. Contains 318158 sequences. (Running on oeis4.)