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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• 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).

Programs

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 *)

PARI

a(n)=9 \\ Charles R Greathouse IV, Oct 07 2015

Scala

List.fill(100)(9) // Alonso del Arte, Jul 08 2018

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