A253513 The characteristic function of the multiples of eight.

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Mikael Aaltonen, Jan 03 2015

Keywords

• nonn
• easy

Comments

Period 8: repeat [1, 0, 0, 0, 0, 0, 0, 0].

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Crossrefs

Cf. A008590 (multiples of 8), A010877, A014025, A168181, A244413.

Programs

Mathematica

Table[Boole[IntegerQ[n/8]], {n, 0, 127}] (* Michael De Vlieger, Jan 03 2015, after Alonso del Arte at A121262 *)
LinearRecurrence[{0,0,0,0,0,0,0,1},{1,0,0,0,0,0,0,0},120] (* or *) PadRight[ {},120,{1,0,0,0,0,0,0,0}] (* Harvey P. Dale, Apr 07 2017 *)
Array[ Boole[ Mod[#, 8] == 0] &, 105, 0] (* Robert G. Wilson v, Oct 08 2017 *)

PARI

A253513(n) = !(n%8); \\ Antti Karttunen, Oct 08 2017

Python

def A253513(n): return int(not(n&7)) # Chai Wah Wu, Jul 09 2022

Formula

a(n) = floor(n/8) - floor((n-1)/8).

a(n) = sin((sin(Pi*(n+1)/2)^2)*Pi*(n+2)/4)/2 + (sin(Pi*(n+1)/2)^2)/4 + sin(Pi*(n+1)/2)/4.

a(n) = abs(A014025(n)).

From Alois P. Heinz, Jan 03 2015: (Start)

a(n) = 1 - A168181(n).

G.f.: 1/(1-x^8). (End)