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

0,2

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

Links

Table of n, a(n) for n=0..86.

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

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)

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A099646 A181693 A271880 * A291092 A010734 A066568

Adjacent sequences: A180596 A180597 A180598 * A180600 A180601 A180602

Keyword

easy,nonn

Author

Odimar Fabeny, Sep 10 2010

Extensions

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

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

Status

approved