Friedman numbers
- What are you reading?
- Did you know that 3685 = ( 36 + 8 ) * 5?
- My wife told me the other day.
- Some kind of wife!
- She is imaginary!
- Oh, mine is complex.
- Aren’t these numbers called Friedman numbers?
- Yes, but why?
- All it says in the book is this:
A Friedman number is a positive integer which can be written in some non-trivial way using its own digits, together with the symbols + – x / ^ ( ) and concatenation. For example, 25 = 52 and 126 = 21 * 6.
- Is 1285 a Friedman number?
- Yes.
- How do you know?
- I am not allowed to tell.
January 28th, 2012 at 9:51 am
The expression for 3685 is particularly nice because the digits were used in the same order as in the original number. That makes it an orderly Friedman number. So is 1285:
1285 = (1+2^8)*5.
January 28th, 2012 at 9:56 am
I would suggest to call it an ordered Friedman number, since you do not even need to rearrange its digits.
January 28th, 2012 at 10:01 am
Oops , I was late for a few minutes…