A010680 Decimal expansion of 1/11.

0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9

Offset

0,2

Comments

Period 2: repeat [0,9].

Links

Table of n, a(n) for n=0..103.

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

Formula

a(n) = (9/2)*(1 - (-1)^n) = 9*(n mod 2). - Paolo P. Lava, Oct 31 2006

From Elmo R. Oliveira, Jan 15 2024: (Start)

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

a(n) = 3 * A010674(n).

G.f.: 9*x/(1-x^2).

E.g.f.: 9*sinh(x). (End)

a(n) = 9 * A000035(n). - Alois P. Heinz, Jan 16 2024

Example

1/11 = 0.0909090909090909090909090909090909090909090909090909090909...

Mathematica

RealDigits[1/11, 10, 100][[1]] (* Alonso del Arte, Mar 11 2018 *)

Prog

(PARI) a(n) = 9*(n%2); \\ Altug Alkan, Mar 25 2018

Crossrefs

Cf. A000035, A010674.

Bisections give: A000004, A010734.

Sequence in context: A059058 A343587 A021015 * A248724 A371649 A278144

Adjacent sequences: A010677 A010678 A010679 * A010681 A010682 A010683

Keyword

nonn,easy,cons

Author

N. J. A. Sloane

Status

approved