[seqfan] Sum of digits in base -2 and base 4

[Keith F. Lynch]

I just noticed that the sum of the digits of each of the numbers 0
through 13 was the same in base -2 and in base 4.  Why should that be?
There's no obvious pattern linking them.  And the rule is broken with 14.

 0      0 0   0 0
 1      1 1   1 1
 2    110 2   2 2
 3    111 3   3 3
 4    100 1  10 1
 5    101 2  11 2
 6  11010 3  12 3
 7  11011 4  13 4
 8  11000 2  20 2
 9  11001 3  21 3
10  11110 4  22 4
11  11111 5  23 5
12  11100 3  30 3
13  11101 4  31 4
14  10010 2  32 5

Those digit sums are A027615 and A053737.  A276328 and A276332 also
start with those same 13 terms.

Through 100, the base 4 sum of digits agrees with the base -2 sum of
digits 81 times.  Through 1000, they agree 560 times.  Through 10000,
they agree 4891 times.  When they disagree, the latter always exceeds
the former, and does so by a small multiple of 3 (at least through
10000, in which range the maximum difference is 15).