A mathematical phenomenon

It happened during a summernight 1992 in Perth, Australia: I recognized, that the sum of the powers of 2³ upwards, written underneath the other diagonally, that the last digit is shifted to the right by one character is always 9. The amount carried over is added as usual.

The following table shows it clearly:

 3:   8
 4:   16
 5:    32
 6:     64
 7:     128
 8:      256
 9:       512
10:       1024
11:        2048
12:         4096
13:          8192
14:          16384
15:           32768
16:            65536
17:            131072
18:             262144
19:              524288
20:              1048576
-------------------------
      999999999999737856

Thomas Renner proved that statement by showing that the number of leading 9's is heading towards infinity.

You can download the whole mathematical prove (4 pages, in german): PDF [120kB] or DVI [9kB].