Skip to main content
MathOverflow

Return to Answer

Post Made Community Wiki by Todd Trimble
over Q (because without precising the field it is known)
Source Link
Sebastien Palcoux
Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186

  1. The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  2. The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  3. The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  4. The number of distinct values taken by ${\omega}$^${\omega}$^${\dots}$^${\omega}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

  5. The number of transitive permutation groups of degree $n$: A002106$(n)$ is conjectured to be the number of Galois groups for irreducible polynomials (over $\mathbb{Q}$) of order $n$ (such groups are transitive). It is a particular case of the Inverse Galois problem.

  1. The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  2. The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  3. The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  4. The number of distinct values taken by ${\omega}$^${\omega}$^${\dots}$^${\omega}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

  5. The number of transitive permutation groups of degree $n$: A002106$(n)$ is conjectured to be the number of Galois groups for irreducible polynomials of order $n$.

  1. The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  2. The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  3. The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  4. The number of distinct values taken by ${\omega}$^${\omega}$^${\dots}$^${\omega}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

  5. The number of transitive permutation groups of degree $n$: A002106$(n)$ is conjectured to be the number of Galois groups for irreducible polynomials (over $\mathbb{Q}$) of order $n$ (such groups are transitive). It is a particular case of the Inverse Galois problem.

a new example about transitive permutation groups
Source Link
Sebastien Palcoux
Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186

  • The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  • The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  • The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  • The number of distinct values taken by ${\omega}$^${\omega}$^${\dots}$^${\omega}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

  1. The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  2. The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  3. The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  4. The number of distinct values taken by ${\omega}$^${\omega}$^${\dots}$^${\omega}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

  5. The number of transitive permutation groups of degree $n$: A002106$(n)$ is conjectured to be the number of Galois groups for irreducible polynomials of order $n$.

  • The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  • The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  • The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  • The number of distinct values taken by ${\omega}$^${\omega}$^${\dots}$^${\omega}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

  1. The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  2. The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  3. The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  4. The number of distinct values taken by ${\omega}$^${\omega}$^${\dots}$^${\omega}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

  5. The number of transitive permutation groups of degree $n$: A002106$(n)$ is conjectured to be the number of Galois groups for irreducible polynomials of order $n$.

mistake fixed
Source Link
Sebastien Palcoux
Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186

  • The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  • The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  • The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  • The number of distinct values taken by ${\omega^{\omega^{.^{.^{.^{\omega}}}}}}$${\omega}$^${\omega}$^${\dots}$^${\omega}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

  • The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  • The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  • The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  • The number of distinct values taken by ${\omega^{\omega^{.^{.^{.^{\omega}}}}}}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

  • The least prime $p$ such that $p+2n$ is also prime: A020483$(n)$, and the smallest number $x$ such that $\sigma(x+2n) = \sigma(x)+2n$: A054906$(n)$.

  • The smallest prime in which a digit appears $n$ times: A084673$(n)$, and the smallest prime containing exactly $n$ $1$'s: A037055$(n)$, for $n>1$.

  • The number of subwords of length $n$ in the infinite word generated by $a \to aab, \ b \to b$ : A006697$(n)$, and the maximal number of distinct nonempty substrings of any binary string of length $n$, plus one: A094913$(n)+1$.

  • The number of distinct values taken by ${\omega}$^${\omega}$^${\dots}$^${\omega}$ (with $n$ $\omega$'s and parentheses inserted in all possible ways) where $\omega$ is the first transfinite ordinal omega: A199812$(n)$, and the number of unlabeled rooted trees with at most $n$ nodes A087803$(n)$, minus $n$ plus one: A255170$(n)$.

minor edit
Source Link
Sebastien Palcoux
Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186
Source Link
Sebastien Palcoux
Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186