[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A086999
Periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.
3
142857, 90, 769230, 5882352941176470, 526315789473684210, 4347826086956521739130, 3448275862068965517241379310, 2127659574468085106382978723404255319148936170
OFFSET
1,1
COMMENTS
A087001(n)=floor(a(n)/10^A087000(n)), A087002(n)=a(n) mod 10^A087000(n);
A087001(n) + A087002(n) = 10^A087000(n) - 1;
a(n) = A087001(n)*10^A087000(n) + A087002(n).
REFERENCES
H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, Die periodischen Dezimalbrueche.
LINKS
Eric Weisstein's World of Mathematics, Decimal Expansion
Eric Weisstein's World of Mathematics, Repeating Decimal
Eric Weisstein's World of Mathematics, Midy's Theorem
EXAMPLE
p=73: a(11)=A060283(21)=13698630 -> [1369][8630] ->
A087001(11)=1369, A087002(11)=8630, A087001(11)+A087002(11)=1369+8630=9999.
CROSSREFS
a(n)=A060283(A049084(A0A028416(n))), A002283.
Sequence in context: A204287 A256630 A263037 * A175694 A023089 A166320
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Jul 29 2003
STATUS
approved