A021823 Decimal expansion of 1/819.

0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

Comments

Partial sums of A010892. - Paul Barry, Jun 06 2003

Expansion in any base b >= 3 of 1/((b-1)*(b^2-b+1)) = 1/(b^3-2b^2+2b-1). E.g., 1/14 in base 3, 1/39 in base 4, 1/84 in base 5, etc. - Franklin T. Adams-Watters, Nov 07 2006

a(n) is the second least significant digit in the ternary representation of 2^n (cf. A004642). - Alexandre Herrera, Oct 09 2023

Examples

			0.0012210012210012210...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

Crossrefs

Cf. A077859, A027444.

Cf. A004642, A153130 (2^n mod 9).

Programs

Mathematica

Join[{0,0},RealDigits[1/819,10,120][[1]]] (* or *) PadRight[{},120,{0,0,1,2,2,1}] (* or *) LinearRecurrence[{2,-2,1},{0,0,1},120] (* Harvey P. Dale, Aug 19 2012 *)

PARI

a(n)=1/819. \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = a(n-1)-a(n-2)+1 = 2-a(n-3) = a(n-6). - Henry Bottomley, Apr 12 2000

a(n) = Sum_{k=1..floor(n/2)} (-1)^(k+1)*binomial(n-k, k) = 1-((-1)^floor(n/3)+(-1)^(floor((n+1)/3)))/2. - Vladeta Jovovic, Feb 10 2003

G.f.: x^2/(1-2x+2x^2-x^3)=x^2/((1-x)(x^2-x+1)). - Paul Barry, Jun 06 2003

a(n+2) = sum{k=0..n, binomial(n-2k, n-k)}. - Paul Barry, Jan 15 2005

a(0)=0, a(1)=0, a(2)=1, a(n)=2*a(n-1)-2*a(n-2)+a(n-3). - Harvey P. Dale, Aug 19 2012