This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225488 #9 May 13 2013 00:30:39 %S A225488 9,45,3,225,18,15,-1,1125,1,99,495,33,2475,198,165,-1,12375,11,999, %T A225488 4995,333,24975,1998,1665,-1,124875,111,9999,49995,3333,249975,19998, %U A225488 16665,-1,1249875,1111,99999,49995,33333,2499975,199998,166665,-1,12499875,11111,999999,4999995,333333,24999975,1999998,1666665,-1,124999875,111111 %N A225488 Murai Chuzen numbers. %C A225488 "Murai Chuzen divides 9 by 1, 2, 3, 4, 5, 6, 7, 8, 9, getting the figures 9, 45, 3, 225, 18, 15, x (not divisible), 1125, 1, -- without reference to the decimal points. Similarly he divides 99 by 1, 2, 3, 4, 5, 6, 7, 8, 9, getting the figures 99, 495, 33, 2475, 198, 165, x, 12375, 11. Next he divides 999 by 1, 2, 3, 4, 5, 6, 7, 8, 9, getting the figures 999, 4995, 333, 24975, 1998, 1665, x, 124875, 111." (Smith and Mikami, expanded and corrected) %C A225488 Smith and Mikami put "x" whenever a decimal does not terminate. In the data, I put -1 instead of "x". %C A225488 Murai Chuzen concludes that if 1 is divided by 9, 45, 3, 225, 18, 15, 1125, and 1, the results will have one-digit repetends; if 1 is divided by 99, 495, 33, 2475, 198, 165, 12375, and 11, the results will have two-digit repetends; if 1 is divided by 999, 4995, 333, 24975, 1998, 1665, 124875, and 111, the results will have three-digit repetends; etc. %D A225488 Murai Chuzen, Sampo Doshi-mon (Arithmetic for the Young), 1781. %H A225488 David Eugene Smith and Yoshio Mikami, <a href="http://books.google.com/books?id=J1YNAAAAYAAJ&pg=PA176&lpg=PA176&dq=%22his+theory+is+brief%22&source=bl&ots=SXl7pxSOKl&sig=we-Nb2Ih5F6QxT2LTPAWQxfhqaQ&hl=en&sa=X&ei=8wmNUaqsO8jr0QGzxIDwBg&ved=0CBoQ6AEwAQ#v=onepage&q=%22his%20theory%20is%20brief%22&f=false">A history of Japanese mathematics</a>, Open Court, 1914, reprinted by Dover, 2004, p. 176. %e A225488 9/1 = 9, so a(1) = 9; 9/2 = 4.5, so a(2) = 45; 9/7 does not terminate, so a(7) = -1; 9/8 = 1.125, so a(8) = 1125; 9/9 = 1, so a(9) = 1. %e A225488 99/1 = 99, so a(10) = 99; 99/2 = 49.5, so a(11) = 495. %Y A225488 Cf. A001913, A007732, A066799, A096688, A121090, A121341, A181431. %K A225488 base,sign %O A225488 1,1 %A A225488 _Jonathan Sondow_, May 10 2013