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

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

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

Examples

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

Crossrefs

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

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

Programs

Mathematica

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

PARI

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

Formula

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