Consider numbers like 343 or 2592.
343=(3+4)^3
2592=2^5*9^2.

We have just shown that some numbers stay unchanged when a number of mathematical operators are added /inserted, without changing the order of the digits.
Within our puzzle lets call those numbers expressionist numbers.
Let us limit the set of acceptable mathematical symbols to the following operators: +, -, *, /, ^, sqrt, !. and any amount of brackets.

My questions:
In the period between 10 A.D. & 2016 A.D. what years were labeled by expressionist numbers?
How many such years will there be between 2017 A.D. & 9999 A.D.?

Bonus: How about one, two (or more) 5-digit examples?

Not much to add. A pair of interesting numbers under 2016 and some other over. 

Edited on May 31, 2016, 7:36 am

Posted by armando on 2016-05-31 07:32:43