Number of \(0\)'s in the binary… to Alternating sum of fourth…
- Number of \(0\)'s in the binary expansion of \(n^2\)
- Smallest deficient multiplier for non-deficiency
- Number of primes between \(n^3 - n\) and \(n^3\)
- Number of primes between \(n^2\) and \(n^2 + (\log_2 n)^2\)
- Recurrence \(a(n+1) = 2n(n+1)a(n) - n^4 a(n-1)\) and associated polynomials
- Smallest integer \(s > n\) such that \(1 + 2s + 3s^2 + \dots + n s^{n-1}\) is prime
- Partitions \(n = x + y\) with \(x^2 + xy + y^2\) prime
- Partitions \(2n + 1 = x + y\) with \(x^4 + y^4\) prime
- Primes \(p < n\) with \(n^2 - n + p\) and \(n^2 + n - p\) prime
- Representations of \(n\) using prime pairs with prime gaps of \(6\)
- Partitions of \(n\) into \(x + y\) with \((xy)^2 + 1\) prime
- Partitions of \(n\) into \(x + y\) with \((xy)^2 + xy + 1\) prime
- A double sum of five binomial factors
- Trajectory of \(64\) under the map \(n \to \text{A006368}(n)\)
- Existence of integers \(k\) with \(k^2 \operatorname{XOR} (k+1)^2 = (2n+1)^2\)
- Determinant of Legendre symbol matrix with factorial shifts
- Representation of sequence terms by harmonic numbers \(\lfloor \frac{1}{2H(n) - H(n^2+n-1) - \gamma} \rfloor\)
- Representations using Sophie Germain primes and twin prime pairs
- Eighth root of the generating function of an Apéry-like sequence
- Alternating sum of fourth powers of binomial coefficients
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