The non-computable sequence: max steps before halting — Σ(n) grows faster than any computable function
Steps taken
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Ones on tape
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Current state
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Σ(n) champion
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Σ(n) = max 1s written by an n-state TM before halting. BB is uncomputable: no algorithm can compute it. BB(5) is known (47,176,870). BB(6) > 10↑↑15. BB(7) is independent of ZFC set theory.