About 10 years ago I published “My house's number” based on a peculiar property of 2592:
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.
9509900499 = 95^0*99^004*99.
(i)Prove that there is infinite number of "printer's glitch" numbers.
(ii) List all such numbers below
(In reply to answer
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
although the sequence excludes possibilities with two ^ in a row and doesn't appear to allow ()
Other variants with more restrictions:
Posted by Jer
on 2015-05-06 10:20:05