This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A155754 #15 Jun 02 2025 01:19:19 %S A155754 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 A155754 -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 A155754 -9,5,-7,6,3,-8,-4,-2,-1,9,-5,7,-6,-3,8,4,2 %N A155754 A variation on 10^n mod 19. %C A155754 This sequence can be employed in a test for divisibility by 19 and works like A033940 works for 7. %C A155754 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 A155754 The test is successful if the final sum is 0. %C A155754 The negative coefficients have the form (10^n mod 19) - 19 when 10^n mod 19 > 9. %C A155754 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 A155754 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,-1). %F A155754 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] %Y A155754 Cf. A033940, A119910, A117378. %K A155754 easy,sign %O A155754 0,2 %A A155754 Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 26 2009