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

0,1

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).

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)

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A052434 A369034 A015241 * A014025 A279760 A287457

Adjacent sequences: A253510 A253511 A253512 * A253514 A253515 A253516

Keyword

nonn,easy

Author

Mikael Aaltonen, Jan 03 2015

Status

approved