A021337 Decimal expansion of 1/333.

0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = (1/3)*{4*(n mod 3)-2*[(n+1) mod 3]+[(n+2) mod 3]}. [Paolo P. Lava, Nov 10 2009]

G.f.: 3*x^2/(1 - x^3). - Chai Wah Wu, Jun 21 2016

From Wesley Ivan Hurt, Jul 02 2016: (Start)

a(n) = a(n-3) for n>2.

a(n) = 1 - cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3).

a(n) = 3*(1 - sgn((n+1) mod 3)).

a(n) = 1 + (n mod 3) - ((n+1) mod 3). (End)

Maple

seq(op([0, 0, 3]), n=0..50); # Wesley Ivan Hurt, Jul 02 2016

Mathematica

PadLeft[First@#, Abs@Last@# + Length@First@#]&@RealDigits[N[1/333, 100]] (* Vincenzo Librandi, Jun 22 2016 *)
PadRight[{}, 100, {0, 0, 3}] (* Wesley Ivan Hurt, Jul 02 2016 *)

Prog

(Magma) &cat [[0, 0, 3]^^30]; // Wesley Ivan Hurt, Jul 02 2016

Crossrefs

Sequence in context: A350914 A346607 A095104 * A361824 A293903 A284444

Adjacent sequences: A021334 A021335 A021336 * A021338 A021339 A021340

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved