Ascending descending base… to Factorial distance to nearest…
- Ascending descending base exponent transform of \(2^n\)
- Number of prime powers \(q<=n\) such that also \(q+2\) is a prime power
- Difference between first odd semiprime \(> 2^n\) and \(2^n\)
- Largest odd divisor of \(a(n-1) + \textrm{prime}(n)\)
- Numerator of \(\zeta(4n)/\zeta(2n)^2\) (with \(a(0)=2\) instead of \(-2\))
- Each term is previous term plus floor of harmonic mean of two previous terms.
- Partial sums of \(\binom{2n}{n}^2\)
- \(a(n)\) = the number of values of \(k <= 10^n\) such that \(\sqrt{k(k+1)(k+2)(k+3)+1}\) is prime
- \(a(n) = \sum_{j=1}^{n} (3^j + (-2)^j)\)
- Determinants of 2 X 2 matrices of non-overlapping blocks of 4 consecutive primes
- Number of primes in \(n\)-th row of triangle \(k^2 - k + p_n\)
- Least \(k\) such that cyclotomic polynomial \(\Phi_k(n)\) is prime
- Sum of Fermat number and Mersenne number minus 1: \(2^{2^n} + 2^n - 1\)
- Least \(k \ge 1\) such that \(2 \cdot n^k - 1\) is prime
- Half-Fibonacci sequence
- Ratio of product of GCDs to product of factorials of floor divisions
- Odious primes minus evil primes among first \(n\) primes
- Recurrence involving LCM: \(a(n) = x(n+1)/x(n) - 2\)
- Number of Abelian cubes of length \(3n\) over an alphabet of size 3
- Factorial distance to nearest square
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