Collatz step differences to Number of ways to write $n = x…
- Collatz step differences
- Representations as \(p + 2^x + 7 \cdot 2^y\) with \(p \equiv 5 \pmod 6\)
- Representations as \(p + 2^x + 11 \cdot 2^y\) with \(p \equiv 1 \pmod 6\)
- Smallest \(m\) such that \(n^3 + m^3 + 1\) is prime
- Number of ways to express \(n\) as sum of square, pentagonal, and hexagonal numbers
- Rowland-style prime-generating recurrence
- Chua's Euclidean prime sequence
- Smallest index \(k > n\) such that \((p_k+p_{k+1})/(p_n+p_{n+1})\) is an integer \(\ge 2\)
- Denominators of \(\sum_{k=1}^n \frac{1}{k 2^k}\)
- Recurrence with fourth powers of binomial coefficients
- Central binomial sum \(a(n) = \sum_{k=0}^n (-4)^k \binom{n}{k}^2 \binom{n-k}{k}^2\)
- Central binomial sum \(a(n) = \sum_{k=0}^n \binom{n}{k}^2 \binom{n-k}{k}^2 (-16)^k\)
- Difference of digit sums in base 3 and base 2
- Van Eck's sequence (OEIS A181391)
- Sum of fourth powers of Fibonacci-like binomial coefficients
- Product of two consecutive primes modulo the next prime
- Recurrence with bitwise XOR
- Number of odd primes between \(n^2\) and \((n+1)^2\) with \((n/p) = 1\)
- Coefficients of \(\prod_{k>0} (1 - x^k/k!)\)
- Number of ways to write \(n = x + y\) (\(0 < x < y < n\)) with \(6x \pm 1\) and \(6y \pm 1\) prime
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