Definition: Strictly non-palindromic number or SNP number n is a number not palindromic in any base b with 2 ≤ b ≤ n-2.
Equipped only with the above definition you are asked to perform the following tasks:
1. Show that 47 is a SNP number.
2. Write down the 1st 7 members of an increasing sequence of SNP numbers.
3. Explain the reason for defining b=n-2 as the upper limit.
4. Prove that all SNP numbers above 6 are prime, but not all primes are SNP numbers.
Charlies took care of most of the parts very well, although I would argue that the list should start 1,2,3,4,6...
To be SNP a number must be prime, otherwise, it will look like aa in some base:
Suppose n = ab, but ab = a(b-1)+ a and so n can be written as the two-digit palindrome "aa" as long as a<b-1
For example, 18 is palindrome in two different bases
18 = 2*9 so in base 8 it's 22
18 = 3*6 so in base 5 it's 33
(Note that 4=2*2 and 6=2*3 are the only composites whose only factors besides 1 are equal or 1 apart. Ie. 4=2*2, 6=2*3)
Posted by Jer
on 2018-02-18 13:12:25