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 A076311 #28 Feb 16 2025 08:32:47
%S A076311 0,-5,-10,-15,-20,-25,-30,-35,-40,-45,1,-4,-9,-14,-19,-24,-29,-34,-39,
%T A076311 -44,2,-3,-8,-13,-18,-23,-28,-33,-38,-43,3,-2,-7,-12,-17,-22,-27,-32,
%U A076311 -37,-42,4,-1,-6,-11,-16,-21,-26,-31,-36,-41,5,0,-5,-10,-15,-20,-25,-30,-35
%N A076311 a(n) = floor(n/10) - 5*(n mod 10).
%C A076311 (n==0 modulo 17) iff (a(n)==0 modulo 17); applied recursively, this property provides a divisibility test for numbers given in base 10 notation.
%D A076311 Karl Menninger, Rechenkniffe, Vandenhoeck & Ruprecht in Goettingen (1961), 79A.
%H A076311 Reinhard Zumkeller, <a href="/A076311/b076311.txt">Table of n, a(n) for n = 0..10000</a>
%H A076311 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisibilityTests.html">Divisibility Tests</a>.
%H A076311 Wikipedia, <a href="http://en.wikipedia.org/wiki/Divisibility_rule">Divisibility rule</a>
%H A076311 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).
%F A076311 a(n)= +a(n-1) +a(n-10) -a(n-11). G.f. x *(-5-5*x-5*x^2-5*x^3-5*x^4-5*x^5-5*x^6-5*x^7-5*x^8+46*x^9) / ( (1+x) *(x^4+x^3+x^2+x+1) *(x^4-x^3+x^2-x+1) *(x-1)^2 ). - _R. J. Mathar_, Feb 20 2011
%e A076311 12808 is not a multiple of 17, as 12808 -> 1280-5*8=1240 -> 124-5*0=124 -> 12-5*4=-8=17*(-1)+9, therefore the answer is NO.
%e A076311 Is 9248 divisible by 17? 9248 -> 924-5*8=884 -> 88-5*4=68=17*4, therefore the answer is YES.
%t A076311 Table[Floor[n/10]-5Mod[n,10],{n,0,60}] (* or *) LinearRecurrence[ {1,0,0,0,0,0,0,0,0,1,-1},{0,-5,-10,-15,-20,-25,-30,-35,-40,-45,1},60] (* _Harvey P. Dale_, Dec 21 2014 *)
%o A076311 (Haskell)
%o A076311 a076311 n = n' - 5 * m where (n', m) = divMod n 10
%o A076311 -- _Reinhard Zumkeller_, Jun 01 2013
%o A076311 (Magma) [Floor(n/10)-5*(n mod 10): n in [0..50]]; // _Vincenzo Librandi_, Jun 23 2015
%o A076311 (PARI) a(n)=n\10 - n%10*5 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A076311 Cf. A008599, A076309, A076310, A076312.
%K A076311 sign,easy
%O A076311 0,2
%A A076311 _Reinhard Zumkeller_, Oct 06 2002