A055242 Largest base in which n is not divisible by any of its digits (0 if no such base).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 5, 0, 0, 0, 7, 0, 8, 0, 8, 6, 10, 0, 11, 7, 11, 0, 13, 0, 14, 9, 14, 10, 16, 0, 17, 11, 17, 11, 19, 0, 20, 13, 19, 14, 22, 0, 23, 14, 23, 15, 25, 11, 26, 17, 26, 18, 28, 0, 29, 19, 29, 19, 31, 14, 32, 21, 32, 22, 34, 13, 35, 23, 34, 23, 37, 17, 38

Offset: 1

Author

Henry Bottomley, May 04 2000

Keywords

• base
• nonn

Comments

If n is odd then a(n)<=(n-3)/2 since in base (n-1)/2 it is written 21, in bases (n+1)/2 through to n its first digit is 1 and in bases >n it is just itself as a single digit; and n is divisible by 1 and itself. If n is even then a(n)<=n/3 since in bases >n/3 through to n/2 its first digit is 2, in bases n/2+1 through to n its first digit is 1 and in bases >n it is just itself as a single digit; and n is divisible by 1, 2 and itself

Examples

			a(11)=4 because it is written as 23 in base 4 and 11 is not divisible by 2 or 3; in every base from 5 through to 11 it has a digit 1 and in every base from 12 onwards it is simply digit 'eleven' - 11 is divisible by both 1 and 'eleven'
		

Crossrefs

Cf. A055238-A055242.