%I #18 Dec 19 2020 01:44:40
%S 0,1,2,3,2,3,5,3,3,3,7,4,4,9,4,5,6,13,6,6,6,17,9,7,19,8,8,8,22,11,8,8,
%T 23,11,9,27,11,10,11,29,11,12,12,33,11,11,19,38,11,16,14,41,15,15,13,
%U 40,14,16,16,45,15,23,48,13,20,17,15,48,21,18,53,20,19,20
%N Absolute values of first differences of A283025.
%C In order to compare this sequence and A005185 see the scatterplot in Links section. Note that A283025 is the sequence that focuses on the remainders when sum of first n terms of A005185 is divided by n. Absolute values of first differences of A283025 keeps the main characteristic of A005185 with deviations.
%H Altug Alkan, <a href="/A283360/b283360.txt">Table of n, a(n) for n = 1..10000</a>
%H Altug Alkan, <a href="/A283360/a283360.png">Scatterplot of A005185 and A283360</a>
%H Pavel Trojovský, <a href="https://doi.org/10.1155/2020/1816756">On Some Properties of the Hofstadter-Mertens Function</a>, Nonlinear Dynamics of Complex Systems, Vol. 2020, Article ID 1816756.
%F a(n) = abs(A283025(n+1) - A283025(n)).
%e a(4) = 3 because a(4) = abs(A283025(5) - A283025(4)) = abs(0 - 3) = 3.
%t Block[{a}, a[1] = a[2] = 1; a[n_] := a[n] = a[n - a[n - 1]] + a[n - a[n - 2]]; Abs@ Differences@ MapIndexed[Mod[#1, First[#2]] &, Accumulate@ Array[a[#] &, 75]]] (* _Michael De Vlieger_, Dec 18 2020 *)
%o (PARI) a=vector(1001); a[1]=a[2]=1; for(n=3, #a, a[n]=a[n-a[n-1]]+a[n-a[n-2]]); va = vector(#a, n, sum(k=1, n, a[k]) % n);
%o for (k=1, 1000, print1(abs(va[k+1] - va[k]) ", "));
%Y Cf. A005185, A283025.
%K nonn
%O 1,3
%A _Altug Alkan_, Mar 05 2017