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Hiroyuki Nashida

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#generative ai Open access Sep 2026

A strict improvement of the Terras-type bound for integers with long Collatz stopping times

Preprint. Let T be the shortcut Collatz map and c = 1 - H(1/log2(3)) = 0.05004..., where H is the binary entropy. The Terras bijection between residues modulo 2^K and parity words shows that at most 2^(alpha(1-c)K + o(K)) integers n <= 2^(alpha K) have coefficient stopping time larger than K. We prove that this Terras-...

Hiroyuki Nashida · 0 citations
#generative ai Open access Sep 2026

A strict improvement of the Terras-type bound for integers with long Collatz stopping times

Preprint. Let T be the shortcut Collatz map and c = 1 - H(1/log2(3)) = 0.05004..., where H is the binary entropy. The Terras bijection between residues modulo 2^K and parity words shows that at most 2^(alpha(1-c)K + o(K)) integers n <= 2^(alpha K) have coefficient stopping time larger than K. We prove that this Terras-...

Hiroyuki Nashida · 0 citations

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