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What number comes next in this sequence?
Here are the first four numbers in the sequence:
10, 11, 95, 96, ...
Do you need a few more numbers to help you figure out what comes next? Here are the next six numbers:
... 100, 101, 125, 976, 995, 996, ...
Do you need even more numbers? Here are the next eight numbers:
... 1000, 1001, 1355, 1376, 9625, 9976, 9995, 9996, ...
Oh, you still need more numbers? Okay, here are the next ten numbers:
... 10000, 10001, 10355, 10376, 10625, 99376, 99625, 99976, 99995, 99996, ...
Okay, I'll give you the next twelve numbers in the sequence:
... 100000, 100001, 100355, 100376, 100625, 109376, 990625, 999376, 999625, 999976, 999995, 999996, ...
I'm guessing you might know it by now, but just in case, here are the next fourteen terms:
... 1000000, 1000001, 1000355, 1000376, 1000625, 1009376, 1109376, 9890625, 9990625, 9999376, 9999625, 9999976, 9999995, 9999996, ...
This is every number in the sequence from zero up to 9,999,999. I have generated the next eight numbers, but I stopped there because my BASIC compiler wanted to go into scientific notation when I did certain calculations.
... 10000000, 10000001, 10000355, 10000376, 10000625, 10009376, 10109376, 12890625, ...
Okay ... Now you have all the terms that I calculated up to twenty million. The next number is somewhere in the ninety millions.
Stop here and try to figure out what obscure and somewhat dumb rule that these numbers follow? Here are some hints:
There is no useful purpose to this sequence
There is absolutely no reason to learn this sequence
Do use your calculator. Using your calculator is an absolute necessity unless you've memorized multiplication techniques that I don't know about.
If you really don't know why this sequence works, write to Webmaster (at) Mazes.com and ask me (be sure to mention this webpage).
Eventually, you will be able to find it in "The On-Line Encyclopedia of Integer Sequences" by N. J. A. Sloane, housed at AT&T Bell Labs in Murray Hill, New Jersey, with the assistance of Simon Plouffe at Universite' du Quebec a' Montreal.
Even if you've figured out the sequence on your own, this is a useful tool. To look up a sequence in the Encyclopedia, send mail to <sequences@research.att.com>. In the body of your e-mail, include a line of the form
lookup 10 11 95 96 100
Send that message, then shortly, if they added my sequence to their database by then, you will get back information by e-mail. You can also search for it at the "The On-Line Encyclopedia of Integer Sequences" website (http://www.research.att.com/~njas/sequences/index.html)
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