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 A375746 #17 Nov 10 2024 16:22:34
%S A375746 0,0,-1,-1,0,1,-2,-4,0,3,-4,-5,4,1,-10,-4,3,1,-2,-9,-2,11,-12,-17,11,
%T A375746 0,-13,0,-1,6,-7,-23,8,7,-20,-10,9,8,-25,-14,13,-4,3,-20,-13,34,-35,
%U A375746 -34,26,-8,-13,-6,5,8,-25,-24,1,26,-27,-34
%N A375746 The alternating sum of sequentially decreasing moduli for every positive integer.
%C A375746 It is expected that this sequence will contain all integers, however in the first 25000 terms, there are only 14907 distinct integers, with -39 and 54 being the two 2 digit numbers not appearing in the first 25000 terms. This sequence, while generated in a different manner, appears to be A154585 shifted over one term and without the absolute value taken.
%H A375746 James C. McMahon, <a href="/A375746/b375746.txt">Table of n, a(n) for n = 1..10000</a>
%F A375746 a(n) = Sum_{k=1..n} (-1)^(n-k) * (n mod k).
%F A375746 abs(a(n)) = A154585(n-1) for n>=2.
%e A375746 For n=6, a(6) = (6 mod 6)-(6 mod 5)+(6 mod 4)-(6 mod 3)+(6 mod 2)-(6 mod 1) = 0-1+2-0+0-0 = 1.
%t A375746 Table[Sum[(-1)^(n-k)*Mod[n,k],{k,n}],{n,60}] (* _James C. McMahon_, Oct 18 2024 *)
%Y A375746 Cf. A154585.
%K A375746 easy,sign
%O A375746 1,7
%A A375746 _Lavender Malison_, Aug 26 2024