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  1. My first, favorite and most important sequence, the weights of prime numbers: A117078
    We see prime numbers classified by level and by weight on the graph.

    A117078: a(n) is the smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists ➡️ oeis.org/A117078

    #decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

  2. α ≈ 1/137 is a cross-ratio — a count of quantum heartbeats in an electron's light-crossing time. The Arithmetic Gauge reveals projective invariants surviving the choice between smooth and discrete geometry, and the geometric origin of prime gap randomness. doi.org/10.5281/zenodo.20137343 #Physics #Mathematics #NumberTheory #ProjectiveGeometry #ArithmeticGauge

  3. The Morita p-adic Gamma function skips multiples of p. The ratio of consecutive values is 1 exactly when p divides n -- it reads divisibility directly. But adelic structure cannot factor: index circularity, O(n^2 log n) cost, regularization prevent it. Value: connections to Gauss sums, p-adic L-functions, adelic Riemann Hypothesis. doi.org/10.5281/zenodo.20119699 #Mathematics #Math #NumberTheory #PureMath #Research #AcademicChatter #Mastodon