The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A087001 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A087001

Left half of periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.
(history; published version)

#7 by Russ Cox at Fri Mar 30 18:50:37 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Jul 29 2003

Discussion

Fri Mar 30

18:50

OEIS Server: https://oeis.org/edit/global/246

#6 by Russ Cox at Sun Jul 10 18:16:39 EDT 2011

LINKS

<a href="/Sindx_index/1.html#1overn">Index entries for sequences related to decimal expansion of 1/n.</a>

Discussion

Sun Jul 10

18:16

OEIS Server: https://oeis.org/edit/global/15

#5 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

<a href="/Sindx_1.html#1overn">Index entries for sequences related to decimal expansion of 1/n.</a>

KEYWORD

nonn,base,new

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

LINKS

<a href="http://www.research.att.com/~njas/sequences/Sindx_1.html#1overn">Index entries for sequences related to decimal expansion of 1/n.</a>

KEYWORD

nonn,base,new

#3 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,base,new

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Jul 29 2003

#2 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005

LINKS

<a href="http://www.research.att.com/~njas/sequences/Sindx_1.html#1overn">Index entries for sequences related to decimal expansion of 1/n.</a>

KEYWORD

nonn,base,new

#1 by N. J. A. Sloane at Sat Sep 13 03:00:00 EDT 2003

NAME

Left half of periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.

DATA

142, 9, 769, 58823529, 526315789, 43478260869, 34482758620689, 21276595744680851063829, 16949152542372881355932203389, 163934426229508196721311475409, 1369, 1123595505617977528089

OFFSET

1,1

COMMENTS

a(n) = floor(A086999(n)/10^A087000(n)); A055642(a(n))=A087000(n);

a(n) + A087002(n) = 10^A087000(n) - 1.

REFERENCES

H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, Die periodischen Dezimalbrueche.

LINKS

<a href="http://www.research.att.com/~njas/sequences/Sindx_1.html#1overn">Index entries for sequences related to decimal expansion of 1/n.</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MidysTheorem.html">Midy's Theorem</a>

EXAMPLE

p=17: A086999(4)=5882352941176470 -> [58823529][41176470] ->

A087001(4)=58823529, A087002(4)=41176470,

A087001(4)+A087002(4)=58823529+41176470=99999999.

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jul 29 2003

STATUS

approved