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| Format: | Recurso digital |
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Zenodo
2025
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| Online-Zugang: | https://doi.org/10.5281/zenodo.15357208 |
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Inhaltsangabe:
- <p>This work introduces a Fibonacci‑like sequence Eₙ defined by the recurrence<br>Eₙ = Eₙ₋₁ + (1/7) Eₙ₋₂<br>within a base‑7 framework called Rational Harmonic Arithmetic (RHA). Empirically, the ratio Eₙ₊₁∕Eₙ converges to the algebraic constant r ≈ 1.12678, providing a purely rational model of exponential growth. Each term Eₙ is a rational number whose denominator is 7ⁿ and whose numerator increases in jumps at base‑7 digit‑length thresholds tied to primes. Extending prior RHA rationalizations of π and φ, this construction offers finite, discrete analogues to classical constants. Full documentation includes detailed derivations, worked examples, graphical plots of Eₙ, and a generalization to approximate √2.</p>