Symmetry of digit sum… to Realization of primes $p \equiv…
- Symmetry of digit sum differences \(\operatorname{sign}(S_5(k) - S_1(k))\)
- Step difference bound \(a(n+1) - a(n) \in \{1, 2\}\) in mass-redistribution cellular automata
- Sum of two squares and two central-binomial-type terms
- Sum of two squares, a power of 3, and a power of 5
- Maximality of \(k = 43\) with restricted digit counts in bases \(3 \le b < k\)
- The 2-4-6-8 Conjecture
- Vanishing of bases with \(b^n \equiv -1 \pmod{2n+1}\) for absolute Euler pseudoprimes
- Four-square conjecture with powers of 2, 3, and 5
- Characterization of Carmichael numbers via squarefree denominators \(a(n)\)
- Nonnegativity of the Dirichlet square root of A046644
- Pronic indices for odd coefficients of \(\sum_{n \ge 0} x^n \frac{(1+x^n)^n}{(1+x^{n+1})^{n+1}}\)
- Pronic indices for odd coefficients of \(\sum_{n \ge 0} x^n \frac{(1+x^n)^n}{(1-x^{n+1})^{n+1}}\)
- Tripling until the seed's digits reappear
- Convergence of fraction numerators \(a(n)/b(n)\) to \(e\)
- Bounds on fractional parts \(n r^2 - a(n)\) for \(r = (2+\sqrt{5})/2\)
- Numerator of a sum involving binomial coefficients
- Factor bounds for Fermat numbers
- A factorial ratio analogous to the Catalan numbers
- Primality of continued fraction denominators \(a(n)\) for \(n \ge 3\)
- Realization of primes \(p \equiv \pm 1 \pmod{10}\) by continued fraction denominators
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