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

1,3

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.

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.

Formula

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

Example

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

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 *)

Prog

(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]) ", "));

Crossrefs

Cf. A005185, A283025.

Sequence in context: A174063 A327277 A124459 * A256366 A046147 A251865

Adjacent sequences: A283357 A283358 A283359 * A283361 A283362 A283363

Keyword

nonn

Author

Altug Alkan, Mar 05 2017

Status

approved