A283360 Absolute values of first differences of A283025.

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, 23, 11, 9, 27, 11, 10, 11, 29, 11, 12, 12, 33, 11, 11, 19, 38, 11, 16, 14, 41, 15, 15, 13, 40, 14, 16, 16, 45, 15, 23, 48, 13, 20, 17, 15, 48, 21, 18, 53, 20, 19, 20

Offset: 1

Author

Altug Alkan, Mar 05 2017

Keywords

• nonn

Comments

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.

Examples

			a(4) = 3 because a(4) = abs(A283025(5) - A283025(4)) = abs(0 - 3) = 3.
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000
• Altug Alkan, Scatterplot of A005185 and A283360
• Pavel Trojovský, On Some Properties of the Hofstadter-Mertens Function, Nonlinear Dynamics of Complex Systems, Vol. 2020, Article ID 1816756.

Crossrefs

Cf. A005185, A283025.

Programs

Mathematica

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 *)

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);
for (k=1, 1000, print1(abs(va[k+1] - va[k]) ", "));

Formula

a(n) = abs(A283025(n+1) - A283025(n)).