A068542 -id:A068542 - cp's OEIS frontend

A021733 Decimal expansion of 1/729.

0, 0, 1, 3, 7, 1, 7, 4, 2, 1, 1, 2, 4, 8, 2, 8, 5, 3, 2, 2, 3, 5, 9, 3, 9, 6, 4, 3, 3, 4, 7, 0, 5, 0, 7, 5, 4, 4, 5, 8, 1, 6, 1, 8, 6, 5, 5, 6, 9, 2, 7, 2, 9, 7, 6, 6, 8, 0, 3, 8, 4, 0, 8, 7, 7, 9, 1, 4, 9, 5, 1, 9, 8, 9, 0, 2, 6, 0, 6, 3, 1, 0, 0, 1, 3, 7, 1, 7, 4, 2, 1, 1, 2, 4, 8, 2, 8, 5, 3

Offset: 0

N. J. A. Sloane

729 = 3^6 = 9^3 = 27^2.
Period is 81 = 9^2 (see example for all 81 digits of the repeating part).
Repeating part in the form of 9 X 9 square table:
  1, 3, 7, 1, 7, 4, 2, 1, 1,
  2, 4, 8, 2, 8, 5, 3, 2, 2,
  3, 5, 9, 3, 9, 6, 4, 3, 3,
  4, 7, 0, 5, 0, 7, 5, 4, 4,
  5, 8, 1, 6, 1, 8, 6, 5, 5,
  6, 9, 2, 7, 2, 9, 7, 6, 6,
  8, 0, 3, 8, 4, 0, 8, 7, 7,
  9, 1, 4, 9, 5, 1, 9, 8, 9,
  0, 2, 6, 0, 6, 3, 1, 0, 0.
Note that each column consists of 9 consecutive (cyclically repeated) digits out of 10. The missing digits in columns from left to right are {7, 6, 5, 4, 3, 2, 0, 9, 8}, which form also a cycle of 9 out of 10 consecutive digits in reverse order, all digits except 1. - Alexander Adamchuk, Dec 28 2013

			1/729 = 0.00137174211248285322359396433470507544581618655692729766\
803840877914951989026063100 (period 81). - _Alexander Adamchuk_, Dec 28 2013

Cf. A068542 (period of the fraction 1/3^n).

Cf. A010701 (1/3), A000012 (1/9), A021031 (1/27), A021085 (1/81).

RealDigits[1/729, 10, 100] (* Alexander Adamchuk, Dec 28 2013 *)

PARI
```
1/729. \\ Michel Marcus, Oct 28 2019
```

Equals Sum_{k>=1} (k*(k+1)/2)/10^(k+2). - Davide Rotondo, Jun 11 2025

A021247 Decimal expansion of 1/243.

Original entry on oeis.org

0, 0, 4, 1, 1, 5, 2, 2, 6, 3, 3, 7, 4, 4, 8, 5, 5, 9, 6, 7, 0, 7, 8, 1, 8, 9, 3, 0, 0, 4, 1, 1, 5, 2, 2, 6, 3, 3, 7, 4, 4, 8, 5, 5, 9, 6, 7, 0, 7, 8, 1, 8, 9, 3, 0, 0, 4, 1, 1, 5, 2, 2, 6, 3, 3, 7, 4, 4, 8, 5, 5, 9, 6, 7, 0, 7, 8, 1, 8, 9, 3, 0, 0, 4, 1, 1, 5, 2, 2, 6, 3, 3, 7, 4, 4, 8, 5, 5, 9

Offset: 0

N. J. A. Sloane, Dec 11 1996

Period 27 Repeat: [0, 0, 4, 1, 1, 5, 2, 2, 6, 3, 3, 7, 4, 4, 8, 5, 5, 9, 6, 7, 0, 7, 8, 1, 8, 9, 3]. - Wesley Ivan Hurt, May 25 2014

			0.00411522633744855967078189300411522633744855967078189300411522633744855967078...

Eric Weisstein's World of Mathematics, 243.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A010701 (1/3), A000012 (1/3^2), A021085 (1/3^4), A021733 (1/3^6).

Cf. A068542 (period of the fraction 1/3^n).

Digits:=100; evalf(1/243); # Wesley Ivan Hurt, May 25 2014

RealDigits[1/243, 10, 100, -1][[1]] (* Wesley Ivan Hurt, May 25 2014; corrected by Harvey P. Dale, Jan 23 2019 *)
PadRight[{},120,{0,0,4,1,1,5,2,2,6,3,3,7,4,4,8,5,5,9,6,7,0,7,8,1,8,9,3}] (* Harvey P. Dale, Jan 23 2019 *)

A021247_upto(N=100)={localprec(N+3);digits((1/3^5+1)\.1^N)[^1]} \\ M. F. Hasler, Apr 23 2021

1/243 = 1/3^5. - M. F. Hasler, Apr 23 2021

cp's OEIS Frontend

A021733 Decimal expansion of 1/729.

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