

A055242


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


5



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
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OFFSET

1,11


COMMENTS

If n is odd then a(n)<=(n3)/2 since in base (n1)/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


LINKS

Table of n, a(n) for n=1..79.


EXAMPLE

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. A055238A055242.
Sequence in context: A129821 A126836 A055241 * A200295 A089389 A081550
Adjacent sequences: A055239 A055240 A055241 * A055243 A055244 A055245


KEYWORD

base,nonn


AUTHOR

Henry Bottomley, May 04 2000


STATUS

approved



