Weekend Challenge Sharpened: Missing Positions in Champernowne's Constant

08082015, 02:26 PM
Post: #10




RE: Weekend Challenge Sharpened: Missing Positions in Champernowne's Constant
Hi Gerald,
I'm still puzzling away at this now "week and two weekend" challenge. I have three questions for clarification: 1. Is this a programming challenge or a mathematical challenge? If the solution requires work like Champernowne's proof, then it's a long way beyond the reach of my efforts! (And I suspect Champernowne didn't come up with it in a weekend!) 2. In your initial post you provided code for finding i(n), the index (into Champernowne's Number) of the start of a given integer n. Are you anticipating that the solution to the challenge will need to call this code? 3. When you request a solution "without iterations, recursions, loop etc.", am I correct in assuming that you include the summation function Σ in your "etc."? In my efforts to eliminate iteration, I've been trying to use the formula for the sum of an arithmeticogeometric sequence. It looks promising but I'm stuck with needing to solve m * 10^m = n (where m and n are positive integers). It's easy for a human to solve by inspection for any given n, but so far I'm puzzled to see how to solve it on the calculator without iterating in some way. 

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