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October 2016

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After computing the three constants accurate enough, all that's left to do is verify the five-digit number 46652 can appear first, after 00:36:06. Several of you solved for other lengths, like Andreas Stiller:

 1  digit:                        1: 0:00:06    (3  + 2  + 1  = 6)
 2  digits:                   35: 0:00:38    (19  + 11  + 8  = 38)
 3  digits:                  459: 0:05:01    (13  + 63  + 225  = 301)
 4  digits:                1384: 0:13:38    (325  + 385  + 108  = 818)
 5  digits:              46652: 0:36:06    (1154 + 381 + 631 = 2166)
 6  digits:            029095: 5:00:32    (2599  + 8579  + 6854  = 18032)
 7  digits:          1718077: 9:28:10    (2802  + 12162  + 19126  = 34090)
 8  digits:        39668259: 90:12:04   (103091  + 156219  + 65414  = 324724)
 9  digits:      941873747: 557:22:48  (1188806  + 105732  + 712030  = 2006568)
10  digits:   2087746140: 1568:05:17 (4378359  + 11711  + 1255047  = 5645117)
11  digits: 38898554239: 4864:11:13 (10363250  + 4123950  + 3023873  = 17511073)