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

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

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

Examples

			0.191919191919191919191919191919191919191...
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

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

From Amiram Eldar, Jun 09 2025: (Start)

With offset 1:

Multiplicative with a(2^e) = 9, a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-3)). (End)