A010734 Constant sequence: the all 9's sequence.

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, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset

0,1

Comments

Continued fraction expansion of (9 + sqrt(85))/2. - Bruno Berselli, Mar 15 2011

Also decimal expansion of 0.9999... = 1. - Jianing Song, Jul 12 2018

Contains "SUB[48]: 200 Terabytes of nines", proposed in Randall Munroe's xkcd Web Comic #2016 as a subsequence. - Hugo Pfoertner, Jul 15 2018

Also digits of the 10-adic integer -1. - Stefano Spezia, Jan 21 2021

Links

Table of n, a(n) for n=0..104.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1017

Tanya Khovanova, Recursive Sequences

Randall Munroe, OEIS Submissions, xkcd Web Comic #2016, Jul 06 2018.

Anderson Norton and Michael Baldwin, Does 0.999... really equal 1?, The Math Educ. 21 (2) (2012) 58-67.

Index to divisibility sequences

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

Formula

G.f.: 9/(1-x). - Bruno Berselli, Mar 15 2011

Equals A158289(n) + A199264(n). - Arkadiusz Wesolowski, Nov 30 2011

E.g.f.: 9*e^x. - Vincenzo Librandi, Jan 26 2012

Mathematica

Table[9, {81}] (* Arkadiusz Wesolowski, Nov 30 2011 *)
IntegerDigits[10^100 - 1] (* Alonso del Arte, Jul 09 2018 *)
PadRight[{}, 120, 9] (* Harvey P. Dale, Jan 28 2020 *)

Prog

(PARI) a(n)=9 \\ Charles R Greathouse IV, Oct 07 2015
(Scala) List.fill(100)(9) // Alonso del Arte, Jul 08 2018

Crossrefs

Sequence in context: A271880 A180599 A291092 * A066568 A291514 A106326

Adjacent sequences: A010731 A010732 A010733 * A010735 A010736 A010737

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved