a is divisible by 1 ab is divisible by 2 abc is divisible by 3 abcd is divisible by 4 abcde is divisible by 5 abcdef is divisible by 6 abcdefg is divisible by 7 abcdefgh is divisible by 8 abcdefghi is divisible by 9 abcdefghij is divisible by 10 http://oeis.org/A111456 http://oeis.org/A256112 I was initially confused about the difference between these two sequences. The second one relaxes the divisibility criteria slightly by not insisting that the entire number be divisible by the base. If it is divisible by the base, that base is even and the number (in BaseForm) ends in 0. Otherwise, it appears that for even bases the final digit is base-1 and for odd bases, (base-1)/2. See: http://chesswanks.com/num/a256112.pdf For bases > 10, the convention a=10, b=11, c=12, .. is used. The ten A111456 terms are highlighted.