Adding a number to a number?

Hi all
I am trying to get a number (entered from a display dialog) , say 12345 to add 1 to it's self giving the number 12346, then have the number 12346 have one added to it giving the number 12347 and so on, this is to be done 35 times, including the origional number, ending up with 12345, 12346, 12347 etc upto 12380.
The number in the dialog will be random each time but will need to have one added to it as above, the result will eventualy be printed.
any suggestions as to how this may be done please.
Cheers
Budgie

Similar to Niel's but with a slightly different repeat, different dialog, and gratuitous tell block:
click here to open this script in your editor<pre style="font-family: 'Monaco', 'Courier New', Courier, monospace; overflow:auto; color: #222; background: #DDD; padding: 0.2em; font-size: 10px; width:400px">set x to {}
tell text returned of (display dialog "Enter a start number:" default answer "12345") to repeat with i from it to it + 35
copy i to end of x
end
choose from list x</pre>

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