login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A021893 Decimal expansion of 1/889. 0
0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5, 9, 2, 8, 0, 0, 8, 9, 9, 8, 8, 7, 5, 1, 4, 0, 6, 0, 7, 4, 2, 4, 0, 7, 1, 9, 9, 1, 0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5, 9, 2, 8, 0, 0, 8, 9, 9, 8, 8, 7, 5, 1, 4, 0, 6, 0, 7, 4, 2, 4, 0, 7, 1, 9, 9, 1, 0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Sum_{i=0}^{infty} [tribonacci(i) / 10^(i+1)].

Generalization: [since tribonacci(i+3) =

  tribonacci(i+2) + tribonacci(i+1) + tribonacci(i)]

  1/889 = Sum_{i=0}^{infty} [tribonacci(i) / 10^(i+1)], (this sequence)

  1/989899 = Sum_{i=0}^{infty} [tribonacci(i) / 100^(i+1)],

  1/998998999 = Sum_{i=0}^{infty} [tribonacci(i) / 1000^(i+1)],

  1/999899989999 = Sum_{i=0}^{infty} [tribonacci(i) / 10000^(i+1)],

  ...

  1 / [(10^k)^3 - (10^k)^2 - (10^k)^1 - (10^k)^0] = 1 / [10^(3k) - 10^(2k) - 10^k - 1] = Sum_{i=0}^{infty} [tribonacci(i) / (10^k)^{i+1}], k >= 1. - Daniel Forgues, May 04 2013

Sum_{i=0}^{infty} [111^i / 1000^(i+1)].

Generalization: [since 111^(i+1) = 111 * 111^(i)]

1/889 = Sum_{i=0}^{infty} [111^i / 1000^(i+1)], (this sequence)

1/9889 = Sum_{i=0}^{infty} [111^i / 10000^(i+1)],

1/99889 = Sum_{i=0}^{infty} [111^i / 100000^(i+1)],

1/999889 = Sum_{i=0}^{infty} [111^i / 1000000^(i+1)],

...

1 / [(10^k)^1 - 111 (10^k)^0] = 1 / [10^k - 111] =

  Sum_{i=0}^{infty} [111^i / (10^k)^(i+1)], k >= 3.

- Daniel Forgues, May 04 2013

LINKS

Table of n, a(n) for n=0..98.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).

FORMULA

From Chai Wah Wu, Feb 03 2021: (Start)

a(n) = a(n-1) - a(n-21) + a(n-22) for n > 21.

G.f.: (-x^21 - 8*x^20 + 8*x^18 - 6*x^17 + 7*x^16 - 4*x^15 + 2*x^14 - 2*x^13 - 3*x^12 + 7*x^11 - 6*x^10 + 6*x^9 - 4*x^8 + 3*x^7 - 4*x^6 - 2*x^5 - x^4 - x^2)/(x^22 - x^21 + x - 1). (End)

MATHEMATICA

Join[{0, 0}, RealDigits[1/889, 10, 120][[1]]] (* or *) PadRight[{}, 120, {0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5, 9, 2, 8, 0, 0, 8, 9, 9, 8, 8, 7, 5, 1, 4, 0, 6, 0, 7, 4, 2, 4, 0, 7, 1, 9, 9, 1}] (* Harvey P. Dale, Dec 02 2018 *)

CROSSREFS

Cf. A000073.

Sequence in context: A165669 A227818 A300890 * A036117 A307357 A116624

Adjacent sequences:  A021890 A021891 A021892 * A021894 A021895 A021896

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 22 07:26 EDT 2021. Contains 343163 sequences. (Running on oeis4.)