From: ThoML Date: 2008-05-05T23:05:02+09:00 Subject: Re: Reverse Divisible Numbers (#161) > Some counter-examples: I didn't mean "derive" in a mathematical sense. I rather had something like the following in mind (I assume you can see a certain regularity) and I suspected that one could define some sort of productions rules to get from one number to the next (not necessarily the next in line but to one or more number(s) below so that no number is left out) without actually doing the maths (just a guess but this is okay for me when I'm sick in bed): $ ruby19 s_marcelo.rb 10_000_000_000_000_000 |grep 10 1089 -- 9801 10989 -- 98901 109989 -- 989901 1099989 -- 9899901 10891089 -- 98019801 10999989 -- 98999901 108901089 -- 980109801 109999989 -- 989999901 1089001089 -- 9801009801 1098910989 -- 9890198901 1099999989 -- 9899999901 10890001089 -- 98010009801 10989010989 -- 98901098901 10999999989 -- 98999999901 108900001089 -- 980100009801 108910891089 -- 980198019801 109890010989 -- 989010098901 109989109989 -- 989901989901 109999999989 -- 989999999901 1089000001089 -- 9801000009801 1089109891089 -- 9801989019801 1098900010989 -- 9890100098901 1099890109989 -- 9899010989901 1099999999989 -- 9899999999901 10890000001089 -- 98010000009801 10890108901089 -- 98010980109801 10891099891089 -- 98019899019801 10989000010989 -- 98901000098901 10989108910989 -- 98901980198901 10998900109989 -- 98990100989901 10999891099989 -- 98999019899901 10999999999989 -- 98999999999901 108900000001089 -- 980100000009801 108901098901089 -- 980109890109801 108910999891089 -- 980198999019801 109890000010989 -- 989010000098901 109891098910989 -- 989019890198901 109989000109989 -- 989901000989901 109998901099989 -- 989990109899901 109999999999989 -- 989999999999901 1089000000001089 -- 9801000000009801 1089001089001089 -- 9801009801009801 1089010998901089 -- 9801098990109801 1089108910891089 -- 9801980198019801 1089109999891089 -- 9801989999019801 1098900000010989 -- 9890100000098901 1098901089010989 -- 9890109801098901 1098910998910989 -- 9890198990198901 1099890000109989 -- 9899010000989901 1099891089109989 -- 9899019801989901 1099989001099989 -- 9899901009899901 1099998910999989 -- 9899990198999901 1099999999999989 -- 9899999999999901 If this worked, the values with the prefix 21 would then derive from 2178 which is 1089 * 2.