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 Printer's glitch (Posted on 2015-05-05)
About 10 years ago I published “My house's number” based on a peculiar property of 2592: 2592=2^5*9^2.

There are additional numbers fitting the definition below:

a. The number is a positive integer of more than 1 digit.
b. Its value remains unchanged if some of the operations ^,* are introduced between its digits.
c. Absence of any of the above signs between 2 adjacent digits signifies their concatenation.
d. Leading zeroes within an exponent are allowed.
e. Brackets may be added to define the order of operations.

Examples:
34425=3^4*425=81*425=34425;
9509900499 = 95^0*99^004*99.

(i)Prove that there is infinite number of "printer's glitch" numbers.
(ii) List all such numbers below 400,000.

 No Solution Yet Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: answer | Comment 3 of 4 |

No.  Friedman numbers are much more plentiful because you can use more operations and re-order the digits.

For printer's glitch numbers in Ady's problem here we are restricted to only * and ^ and () are allowed and the digits must stay in order.
The problem is most like
https://oeis.org/A156322
although the sequence excludes possibilities with two ^ in a row and doesn't appear to allow ()

Other variants with more restrictions:
https://oeis.org/A116890
https://oeis.org/A096298

 Posted by Jer on 2015-05-06 10:20:05

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