  i  size  num  c_i  total   3i  bank  Phi  amortized
  1     1    1    1      1    3     2    1       2
  2     2    2    2      3    6     3    2       3
  3     4    3    3      6    9     3    2       3
  4     4    4    1      7   12     5    4       3
  5     8    5    5     12   15     3    2       3
  6     8    6    1     13   18     5    4       3
  7     8    7    1     14   21     7    6       3
  8     8    8    1     15   24     9    8       3
  9    16    9    9     24   27     3    2       3
 10    16   10    1     25   30     5    4       3
 11    16   11    1     26   33     7    6       3
 12    16   12    1     27   36     9    8       3
 13    16   13    1     28   39    11   10       3
 14    16   14    1     29   42    13   12       3
 15    16   15    1     30   45    15   14       3
 16    16   16    1     31   48    17   16       3
 17    32   17   17     48   51     3    2       3
n =      17:  total cost =      48  <  3n = 51
n =    1000:  total cost =    2023  <  3n = 3000
n = 1000000:  total cost = 2048575  <  3n = 3000000
