A172051 Decimal expansion of 1/999999.

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

Offset: 0

Author

Mats Granvik, Jan 24 2010

Keywords

• nonn
• cons
• easy

Comments

Period 6: repeat [0, 0, 0, 0, 0, 1].

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Crossrefs

Cf. A022003, A172050, A245477.

Programs

Magma

[n mod (1 + ((n-1) mod 3)) : n in [0..100]]; // Wesley Ivan Hurt, Aug 29 2014

Maple

A172051:=n->(n mod (1+((n-1) mod 3))): seq(A172051(n), n=0..100); # Wesley Ivan Hurt, Aug 16 2014

Mathematica

Join[{0,0,0,0,0},RealDigits[1/999999,10,120][[1]]] (* or *) PadRight[ {},120,{0,0,0,0,0,1}] (* Harvey P. Dale, Oct 24 2013 *)

Formula

a(n) = (1-((-1)^A172050(n+4)))/2. A similar formula is given by Hieronymus Fischer in A022003.

a(n) = 1 if (n+1) mod 6 = 0 else 0.

a(n) = A079979(n+1). [R. J. Mathar, Jan 28 2010]

a(n) = (n-2)*(Fibonacci(n-2)-1) mod 2. [Gary Detlefs, Dec 29 2010]

a(n) = n mod (1 + (n-1) mod 3). - Wesley Ivan Hurt, Aug 16 2014

G.f.: x^5/(1-x^6). - Vaclav Kotesovec, Aug 18 2014

a(n) = binomial((5*n+10) mod 6, 5). - Wesley Ivan Hurt, Aug 29 2014

a(n) = 1 - sign((n+1) mod 6). - Wesley Ivan Hurt, Aug 29 2014

a(n) = A245477(n) - 1. - Wesley Ivan Hurt, Aug 29 2014

From Wesley Ivan Hurt, Jun 23 2016: (Start)

a(n) = a(n-6) for n>5.

a(n) = (3 - 3*cos(n*Pi) + 6*cos(n*Pi/3) + 6*cos((n-4)*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3) - 2*sqrt(3)*sin((1+2*n)*Pi/3))/18. (End)