New to the list, so I hope this will go in the right place. But replying to Joerg Arndt’s listing of the first few natural numbers in base 2+i using the digits {0,+1,-1,+i,-i}: The problem with this digit set is that it is not immediately obvious what the rule is to go from number to number adding one. Here is another idea: use the digits {-1,0,1,2,3}. And base 2+i has the carry rule [-1,+4,-5], which says if a digit is 4 or greater, subtract 5 from it, add 4 to the next most significant, subtract one from the next next most significant. One way of verifying this is to see that (-1)(2+i)^{k+2}+4(2+i)^{k+1}-5(2+i)^k=0. For example, with least significant digits on the right, 1 = 1, 2 = 2 3 = 3 4 = (-1)4(-1) = (-1)3(-1)(-1) 5 = (-1)3(-1)0 6 = (-1)3(-1)1 7 = (-1)3(-1)2 8 = (-1)3(-1)3 9 = (-1)3(-1)4 = (-1)23(-1) 10 = (-1)230 11 = (-1)231 12 = (-1)232 13 = (-1)233 14 = (-1)234 = (-1)17(-1) = (-2)52(-1) = (-1)202(-1) and so on. A couple of notes: these digits are exactly the same representing natural numbers in base 2-i as well. This is current (!) joint work with Jim Propp on digits representing numbers in different bases simultaneously. And in base 2+i, you can extend the classic work of Katai and Szabo and represent Gaussian integers in base 2+i. If you limit yourself to nonnegative digits, they proved only -n+i works, not n+i. But a negative digit does the job! Steve