login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A224365 Numerators of fractions for Pi. 1
10, 3, 3, 3, 157, 22, 22, 22, 22, 22, 22, 22, 22, 51808, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The repeated terms (3, 22, 355, 5419351,... from A063674) are the numerators of fractions (3/1, 22/7, 355/113, 5419351/1725033,... ) leading to Pi.

(I can't access to every term of A063674)

Zu Chongzhi (5th century) discovered 22/7 and 355/113. Adriaan Anthonisz Metius rediscovered 355/113 in 1585.

A sequence, in which 3, 22, 355, 5419351, 21053343141, 66627445592888887, 2646693125139304345 appear, will be submitted. Note the number of digits: 1, 2, 3, 7, 11, 17, 19.

A063673 differences give the denominators:

3, 1, 1, 1, 50, 7, 7, 7, 7, 7, 7, 7, 7, 16489, 113, 113,... .

Hence 10/3, 157/50, 51808/16489,... .

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..168

FORMULA

a(n) = A063674(n+1) - A063674(n).

MATHEMATICA

A224365 = Reap[ For[ delta0 = 1; d = 1, d < 10^5, d++, delta = Abs[Pi - Round[Pi*d]/d]; If[ delta < delta0, Sow[ Round[Pi*d]]; delta0 = delta]]][[2, 1]] // Differences (* Jean-Fran├žois Alcover, Apr 10 2013 *)

CROSSREFS

Cf. A063673(n+1) - A063673(n). A046947, A072398, A002485. A132049, A003077, A068028, A068079.

Sequence in context: A144859 A280519 A010172 * A087869 A167764 A241887

Adjacent sequences:  A224362 A224363 A224364 * A224366 A224367 A224368

KEYWORD

nonn,less,frac

AUTHOR

Paul Curtz, Apr 09 2013

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 November 11 22:31 EST 2019. Contains 329046 sequences. (Running on oeis4.)