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Interesting leettimes

• Interesting leettime: 18:20 is 620 (18 o'clock is 6 pm)
• Interesting leettime: 18:21 is 93 (1+8, 2+1)
• Interesting leettime: 21:15 is 555
• Interesting leettime: 18:51 is 123
• Interesting leettime: 19:03 is 999
• Interesting leettime: 08:40 is 1000
• The humantime of 1337 is 13:29.

More interesting observations:

• 00:00 am is 0 o'clock leettime, 00:30 is 30, 01:00 is 60, 01:30 is 90, ...
• 00:01 am is 913 o'clock leettime, 00:31 is 943, 01:01 is 973, 01:31 is 1003, ... see the pattern there?
• Given leetime t, the leettime of the next minute is t + 913 MOD 1440.

Background
leettime is built upon exactly 30 residue classes. The representatives are (in ascending order): 0, 13, 26, 9, 22, 5, 18, 1, 14, 27, 10, 23, 6, 19, 2, 15, 28, 11, 24, 7, 20, 3, 16, 29, 12, 25, 8, 21, 4, 17. Each leettime value can be backtraced to one of them by subtracting the closest (smaller) multiple of 30 from it.

Let's have a closer look at these representatives -- more patterns to come:

00:00 0 0       (1) look at the 0 here
00:01 913 13    (2) after that look at the 13
00:02 386 26
00:03 1299 9
00:04 772 22
00:05 245 5
00:06 1158 18 
00:07 631 1     (1) see that 1 is 0+1
00:08 104 14    (2) and 14 is an incremented 13
00:09 1017 27
00:10 490 10
00:11 1403 23
00:12 876 6
00:13 349 19
00:14 1262 2    (1) continuing with the 1
00:15 735 15    (2) 14 + 1 = 15 and so on
00:16 208 28
00:17 1121 11
00:18 594 24
00:19 67 7
00:20 980 20
00:21 453 3
00:22 1366 16
00:23 839 29
00:24 312 12
00:25 1225 25
00:26 698 8
00:27 171 21
00:28 1084 4
00:29 557 17
00:30 30 0