A087001 - OEIS

%I #8 Feb 16 2025 08:32:50

%S 142,9,769,58823529,526315789,43478260869,34482758620689,

%T 21276595744680851063829,16949152542372881355932203389,

%U 163934426229508196721311475409,1369,1123595505617977528089

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

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

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

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

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

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

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

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

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

%K nonn,base

%O 1,1

%A _Reinhard Zumkeller_, Jul 29 2003