(Followup to 982 digit conspiracy:)

After newenigma contributor Ogee turned up some interesting variants in octal, I started looking at non decimal bases myself. One of the best I found is this: In base 15 (with digits 0, 1, 2, 3, … , 9, a, b, c, d, e), eeeeeeeeeeee/d (in decimal, 129746337890624/13) equals 124936dca5b8 (decimal 9980487530048), a 12 digit number with no zeroes and all digits different. Multiply this by any number from 1 to c and you get a cyclic permutation:

x 1 = 124936dca5b8

x 2 = 24936dca5b81

x 4 = 4936dca5b812

x 8 = 936dca5b8124

x 3 = 36dca5b81249

x 6 = 6dca5b812493

x c = dca5b8124936

x b = ca5b8124936d

x 9 = a5b8124936dc

x 5 = 5b8124936dca

x a = b8124936dca5

x 7 = 8124936dca5b

Likewise:

base 20 jjjjjjjjjjjjjjjjjjjj/h = 13abf5hcig984e27

base 21 kkkkkkkkkkkkkkkkkkkkk/j = 1248he7f9jigc36d5b

base 28 rrrrrrrrrrrrrrrrrrrrrrrrrrrr/n = 162c4o9kjdaqlpfn3i78eh

base 31 uuuuuuuuuuuuuuuuuuuuuuuuuuuu/t = 1248h36cpk9j7etsqmdroi5albng

base 34 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx/v = 139tkshilvre8qawuo4d5gfc26jp7n

give cyclic permutations under multiplication by 1, 2, 3 … (denominator-1).

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