A093719 a(n) = (n mod 2)^(n mod 3).

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

Offset: 0

Author

Reinhard Zumkeller, Apr 12 2004

Keywords

• nonn
• easy

Comments

This is a periodic sequence with period 6. The repeating block is 1,1,0,1,0,1. - Michel Dekking, Sep 19 2020

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for characteristic functions
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Crossrefs

Cf. A000035, A010872, A047235, A047273, A093718.

Programs

GAP

List([0..120],n->(n mod 2)^(n mod 3)); # Muniru A Asiru, Dec 19 2018

Magma

[(n mod 2)^(n mod 3): n in [0..100]]; // Wesley Ivan Hurt, Oct 13 2014

Maple

A093719:=n->(n mod 2)^(n mod 3): seq(A093719(n), n=0..40); # Wesley Ivan Hurt, Oct 13 2014

Mathematica

PadRight[{},120,{1,1,0,1,0,1}] (* Harvey P. Dale, Jun 26 2021 *)

PARI

A093719(n) = ((n%2)^(n%3)); \\ Antti Karttunen, Dec 19 2018

Formula

a(n) = A000035(n)^A010872(n).

a(A047273(n)) = 1, a(A047235(n)) = 0. [Reinhard Zumkeller, Oct 01 2008]

G.f.: -(x^5 + x^3 + x + 1)/(x^6 - 1). - Colin Barker, Apr 01 2013

E.g.f.: (2*cos(sqrt(3)*x/2)*cosh(x/2) + cosh(x))/3 + sinh(x). - Stefano Spezia, Jul 26 2024