cp's OEIS Frontend

A086999 Periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.

%I A086999 #9 Feb 16 2025 08:32:50
%S A086999 142857,90,769230,5882352941176470,526315789473684210,
%T A086999 4347826086956521739130,3448275862068965517241379310,
%U A086999 2127659574468085106382978723404255319148936170
%N A086999 Periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.
%C A086999 A087001(n)=floor(a(n)/10^A087000(n)), A087002(n)=a(n) mod 10^A087000(n);
%C A086999 A087001(n) + A087002(n) = 10^A087000(n) - 1;
%C A086999 a(n) = A087001(n)*10^A087000(n) + A087002(n).
%D A086999 H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, Die periodischen Dezimalbrueche.
%H A086999 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DecimalExpansion.html">Decimal Expansion</a>
%H A086999 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RepeatingDecimal.html">Repeating Decimal</a>
%H A086999 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MidysTheorem.html">Midy's Theorem</a>
%H A086999 <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n.</a>
%e A086999 p=73: a(11)=A060283(21)=13698630 -> [1369][8630] ->
%e A086999 A087001(11)=1369, A087002(11)=8630, A087001(11)+A087002(11)=1369+8630=9999.
%Y A086999 a(n)=A060283(A049084(A0A028416(n))), A002283.
%K A086999 nonn,base
%O A086999 1,1
%A A086999 _Reinhard Zumkeller_, Jul 29 2003