A010691 Period 2: repeat (1,10).

1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• word

Comments

Regular continued fraction of (5+sqrt 35)/10. - R. J. Mathar, Nov 21 2011

Sequence is an infinite palindrome in two ways (numbers and English names): ONE, TEN, ONE, TEN, ONE, TEN, ONE, ... . - Eric Angelini, Sep 16 2023

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1).

Crossrefs

Cf. A036117, A070341, A168429, A070367, A070392, A070404, A048271, A187466.

Programs

Magma

[10^n mod 11: n in [0..80]]; // Vincenzo Librandi, Aug 24 2011

Maple

g:=(1+10*z)/((1-z^2)): gser:=series(g, z=0, 66): seq((coeff(gser, z, n)), n=0..65); # Zerinvary Lajos, Feb 25 2009

Mathematica

PadRight[{},100,{1,10}] (* Harvey P. Dale, Aug 27 2013 *)

Formula

a(n) = -9/2*(-1)^n + 11/2.

G.f.: (1+10*z)/(1-z^2). - Zerinvary Lajos, Feb 25 2009

a(n) = 10^n mod 11. - M. F. Hasler, Mar 10 2011

From Nicolas Bělohoubek, Nov 11 2021: (Start)

a(n) = 10/a(n-1). See also A010695.

a(n) = 11 - a(n-1). See also A010712. (End)