Prime numbers at the beginning… to $a(n) = (\text{smallest prime}…
- Prime numbers at the beginning of the 20th century
- \(a(n)\) is the integer whose decimal digits are the first \(n+1\) decimal digits of \(\pi\)
- Denominator of sum of reciprocals of divisors
- A nonlinear recurrence sequence
- Determinant of Hankel matrix of the first \(2n-1\) prime numbers
- Combinatorial representation of the recurrence \(a(n+2) = 2a(n+1) + 2a(n)\)
- Smallest number \(k\) such that \(kn + 1\) is prime
- Smallest prime \(\equiv 1 \pmod n\)
- Home primes (OEIS A037274)
- Number of primes \(< n^3\)
- Number of primes \(< n^2\)
- Conjectures associated with A038552
- Smallest composite \(c\) such that \(\textrm{primorial}(n) + c\) is prime
- Denominators of coefficients in Stirling's expansion for \(\log(\Gamma(z))\)
- \(a(n) = \sum_{k=1}^n (k^2 \bmod n)\)
- Nearest integer to \(n/\sqrt{2}\)
- Asymptotics of subsets of \(\{1, 2, \dots, n\}\) with integer average
- Maximum exponent in the prime factorization of \(n\)
- Expansion of g.f. \((1-\sqrt{1-4x-4x^2})/(2(1+x))\)
- \(a(n) = (\text{smallest prime} > n^2) - n^2\)
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