A308320 - OEIS

A308320

Decimal expansion of 2^(-7/4); exact length of the A4 paper size measured in meters according to the ISO 216 standard.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

Also exact width of the A3 paper size measured in meters.

According to the ISO 216 standard, the A0 paper size is defined to have an area of 1 square meter where the ratio of the length to the width is sqrt(2), so the length is 2^(1/4) m and the width is 2^(-1/4) m. For each n >= 0, the length of the size A(n+1) is equal to the width of the size A(n) and the width of the size A(n+1) is equal to half of the length of the size A(n), so the area of the size A(n+1) is half of that of A(n). Equivalently, the length of the A(n) size is 2^(-n/2 + 1/4) m and the width is 2^(-n/2 - 1/4) m. For the A4 size, the exact length and width are 2^(-7/4) m = 297.301... mm and 2^(-9/4) m = 210.224... mm (A308321), and the actual length and width are 297 mm and 210 mm.

LINKS

Table of n, a(n) for n=0..87.

Prepressure, A4.

Wikipedia, ISO 216.

FORMULA

Equals square root of A222066. - R. J. Mathar, Jan 27 2021

EXAMPLE

0.29730177...

The exact lengths and widths (rounded to the nearest 1/10 mm) and areas of the A-series are as follows:

size | exact length | exact width | exact area (mm^2)

A0 | 2^( 1/4) m = 1189.2 mm | 2^(- 1/4) m = 840.9 mm | 1000000

A1 | 2^(- 1/4) m = 840.9 mm | 2^(- 3/4) m = 594.6 mm | 500000

A2 | 2^(- 3/4) m = 594.6 mm | 2^(- 5/4) m = 420.4 mm | 250000

A3 | 2^(- 5/4) m = 420.4 mm | 2^(- 7/4) m = 297.3 mm | 125000

A4 | 2^(- 7/4) m = 297.3 mm | 2^(- 9/4) m = 210.2 mm | 62500

A5 | 2^(- 9/4) m = 210.2 mm | 2^(-11/4) m = 148.7 mm | 31250

A6 | 2^(-11/4) m = 148.7 mm | 2^(-13/4) m = 105.1 mm | 15625

A7 | 2^(-13/4) m = 105.1 mm | 2^(-15/4) m = 74.3 mm | 7812.5

A8 | 2^(-15/4) m = 74.3 mm | 2^(-17/4) m = 52.6 mm | 3906.25

A9 | 2^(-17/4) m = 52.6 mm | 2^(-19/4) m = 37.2 mm | 1953.125

A10 | 2^(-19/4) m = 37.2 mm | 2^(-21/4) m = 26.3 mm | 976.5625

And the actual lengths, widths and areas (note that the actual areas are always smaller than the exact areas) are as follows:

size | actual length (mm) | actual width (mm) | actual area (mm^2)

A0 | 1189 | 841 | 999949 (99.9949%)

A1 | 841 | 594 | 499554 (99.9108%)

A2 | 594 | 420 | 249480 (99.7920%)

A3 | 420 | 297 | 124740 (99.7920%)

A4 | 297 | 210 | 62370 (99.7920%)

A5 | 210 | 148 | 31080 (99.4560%)

A6 | 148 | 105 | 15540 (99.4560%)

A7 | 105 | 74 | 7770 (99.4560%)

A8 | 74 | 52 | 3848 (98.5088%)

A9 | 52 | 37 | 1924 (98.5088%)

A10 | 37 | 26 | 962 (98.5088%)

MATHEMATICA

RealDigits[2^(-7/4), 10, 88][[1]] (* James C. McMahon, Feb 26 2024 *)

PROG

(PARI) default(realprecision, 100); 2^(-7/4)

CROSSREFS

Cf. A010767 (2^(1/4)), A228497 (2^(-1/4)), A308321 (2^(-9/4)).

Sequence in context: A011070 A230480 A335605 * A254140 A200991 A013500

Adjacent sequences: A308317 A308318 A308319 * A308321 A308322 A308323

KEYWORD

nonn,cons

AUTHOR

Jianing Song, May 20 2019

EXTENSIONS

Edited by Jon E. Schoenfield, Feb 25 2024

STATUS

approved