3 ms·
The Martin Gardner doesn't really seem to fit, since it is trivial to solve using brute force. Even if using a computer is considered cheating, there are shortc
by gweinberg 13y ago
The Martin Gardner doesn't really seem to fit, since it is trivial to solve using brute force. Even if using a computer is considered cheating, there are shortcuts to use to keep from having to try everything. For example, having a "1" digit gets you nowhere, a "0" kills you, and a "5" and any even digit also kills you (and the 5 will persist at the end if you don't have an even digit, so it will probably kill you next round).
This led me to wonder, does persistence ever max out? It seems likely to me that it does.
- crondee 13y agoI dont think it will max out. I brute forced it upto 10 million and I got the following numbers (5, 679) (6, 6788) (7, 68889) (8, 2677889) sure the numbers are exponential but no reason to suspect that a glass ceiling exists.
- peterderivaz 13y agoInterestingly, Wikipedia disagrees. For a radix of 10, there is thought to be no number with a multiplicative persistence > 11: this is known to be true for numbers up to 10 to the power of 50. http://en.wikipedia.org/wiki/Persistence_of_a_number http://en.wikipedia.org/wiki/Persistence_of_a_number I guess the problem is that when you multiply lots of digits together you become increasingly likely to end up with a 0 digit somewhere.
- crondee 13y agoThanks for the link, I dug a little more and came across [1] which mentions a contribution by erdos to the effect that persistence might not be bounded. I guess I might spend some time to figure out number 12 :) [1] http://web.archive.org/web/20050214141815/http://www.wschnei.de/digit-related-numbers/persistence.html http://web.archive.org/web/20050214141815/http://www.wschnei...