A010690 Period 2: repeat (1,9).

1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1

Offset

0,2

Comments

Digital roots of the nonzero square triangular numbers. - Ant King, Jan 21 2012

Continued fraction expansion of A176019. - R. J. Mathar, Mar 08 2012

Exp( Sum_{n >= 1} a(n-1)*x^n/n ) = 1 + x + 5*x^2 + 5*x^3 + 15*x^4 + 15*x^5 + ... is the o.g.f. for A189976 (taken with an offset of 0). - Peter Bala, Mar 13 2015

Final digit of 9^n. - Martin Renner, Jun 11 2020

Decimal expansion of 19/99. - Stefano Spezia, Feb 09 2025

Links

Table of n, a(n) for n=0..80.

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

Formula

G.f.: (1+9x)/((1-x)(1+x)). - R. J. Mathar, Nov 21 2011

a(n) = 9^n mod 10. - Martin Renner, Jun 11 2020

E.g.f.: cosh(x) + 9*sinh(x). - Stefano Spezia, Feb 09 2025

Example

0.191919191919191919191919191919191919191...

Mathematica

5+4*(-1)^# &/@Range[81] (* Ant King, Jan 21 2012 *)

Prog

(PARI) a(n)=1; if(n%2==1, 9, 1) \\ Felix Fröhlich, Aug 11 2014

Crossrefs

Cf. A008592, A001019 (9^n), A014393, A189976.

Sequence in context: A200696 A203130 A209050 * A224835 A329725 A339354

Adjacent sequences: A010687 A010688 A010689 * A010691 A010692 A010693

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved