A180599 Zero followed by infinitely many 9's.

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

Offset: 0

Author

Odimar Fabeny, Sep 10 2010

Keywords

• easy
• nonn

Comments

Another interpretation: A real number with an infinitesimally small difference from the integer 1 which is used to test the precision of calculating devices. - John W. Nicholson, Feb 01 2012

a(n) is also the number of n-digit positive repdigit numbers (A010785). - Stefano Spezia, Aug 15 2020

Examples

			Viewed as a real number: For a TI-89, entering 1.-10^-12 yields .999999999999; however, 1.-10^-13 yields 1. - _John W. Nicholson_, Feb 01 2012
		

Links

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

Crossrefs

Cf. A007953, A010785, A010888, A057427, A180592, A180594, A180595, A180596, A180597, A180598.

Programs

Mathematica

a[n_] := Mod[9 n - 1, 9] + 1; a[0] = 0; Array[a, 105, 0] (* Robert G. Wilson v, Sep 20 2010 *)
PadRight[{0},120,9] (* Harvey P. Dale, May 03 2019 *)

PARI

a(n)=if(n,9,0) \\ Charles R Greathouse IV, Jan 04 2013

Formula

a(0) = 0, a(n) = 9 for n > 0.

a(n) = 9 * A057427(n).

a(n) = A010888(9*n), where A010888 is the digital root.

From Robert Israel, Dec 16 2014: (Start)

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

E.g.f.: 9*(exp(x) - 1). (End)

Extensions

More terms from Robert G. Wilson v, Sep 20 2010

Definition changed by N. J. A. Sloane, Feb 04 2012