A199264 -id:A199264 - cp's OEIS frontend

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

N. J. A. Sloane

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

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).

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 *)

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

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

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

A262734 Period 16: repeat (1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9

Offset: 0

Ilya Gutkovskiy, Sep 29 2015

Decimal expansion of 111111112/900000009.

For n which lies in the interval [16*(k-1), 8*(2*k-1)], where k>0 -> pattern {1, 2, 3, 4, 5, 6, 7, 8, 9}; for n which lies in the interval [16*k - 7, 16*k - 1], where k>0 -> pattern {8, 7, 6, 5, 4, 3, 2}.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,-1,1).

Cf. A158289, A177274, A010889, A138531, A181975, A199264, A068073, A028356.

&cat[[1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2]: n in [0..10]]; // Vincenzo Librandi, Sep 29 2015

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, -1, 1}, {1, 2, 3, 4, 5, 6, 7, 8, 9}, 120] (* Vincenzo Librandi, Sep 29 2015 *)

Vec(-(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/((x-1)*(x^8+1)) + O(x^100)) \\ Colin Barker, Sep 29 2015

111111112/900000009. \\ Altug Alkan, Sep 29 2015

vector(200, n, default(realprecision, n+2); floor(111111112/900000009*10^n)%10) \\ Altug Alkan, Nov 12 2015

-1 + a(16*(k - 1)) = -2 + a(8*k + 3*(-1)^k - 4) = -3 + a(2*(4*k + (-1)^k - 2)) = -4 + a(8*k + (-1)^k - 4) = -5 + a(4*(2*k - 1)) = -6 + a(8*k - (-1)^k - 4) = -7 + a(-2*(-4*k + (-1)^k + 2)) = -8 + a(8*k - 3*(-1)^k - 4) = -9 + a(8*(2*k - 11)) = 0, for k>0.
a(0) = 1, a(n) = a(n+1) - 1, for 16*(k - 1) <= n < 8*(2*k - 1), and a(n) = a(n + 1) + 1, for 8*(2*k - 1) <= n < 16*k, where k>0.
From Colin Barker, Sep 29 2015: (Start)
a(n) = a(n-1) - a(n-8) + a(n-9) for n>8.
G.f.: -(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)*(x^8+1)). (End)

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A010734 Constant sequence: the all 9's sequence.

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A262734 Period 16: repeat (1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2).

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