Volume 10, Issue 2 Articles In and Out Trott's Corner Beyond Sudoku New Products New Publications Calendar News Bulletins New Resources Classifieds Download This Issue Editorial Policy Staff and Contributors Submissions Subscriptions Advertising Back Issues Contact Information 
T R O T T ' S C O R N E R
Why Searches Are DifficultLochs' theorem [2] states that to represent a decimal number with digits, we need about simple continued fraction terms. This means that when adding digits to our lists, the continued fraction digits and the radix digits get slowly out of sync. To ensure that the digits agree with each other, we need a pool size that becomes progressively larger. Lochs' theorem holds in its classic form only for simple continued fractions. But experience shows that nonsimple continued fractions behave similarly. Let us analyze the best Trott constant found with more than 400 coinciding digits.
On average we obtain about 0.7 decimal digits per continued fraction digit.
The following graphics show the digit gain and the difference of the digit gain and its linear part.
The absolute difference shows similar behavior, though different in detail.


About Mathematica  Download Mathematica Player © Wolfram Media, Inc. All rights reserved. 