  n   T(n)  2n   U(n)  2n-1
  1      1   2      1     1
  2      3   4      3     3
  3      4   6      3     5
  4      7   8      7     7
  5      8  10      7     9
  6     10  12      7    11
  7     11  14      7    13
  8     15  16     15    15
  9     16  18     15    17
 10     18  20     15    19
n <= T(n) <= 2n     fails for 0 values of n up to 10^6
U(n) <= 2n - 1      fails for 0 values of n up to 10^6
U(n) <= n (c = 1)   fails for 999981 values, the first at n = 2
