Problems · OpenFrontiers

OP-9883Number theoryStatus unassessed

Concatenation of the next $n$ numbers

Concatenation of the next n numbers

Formal Conjectures· Specialist source · status unassessed

OP-9882Number theoryStatus unassessed

$a(n) = (\text{smallest prime} > n^2) - n^2$

a(n) = ( text smallest prime n^2) - n^2

Formal Conjectures· Specialist source · status unassessed

OP-9881CombinatoricsStatus unassessed

Expansion of g.f. $(1-\sqrt{1-4x-4x^2})/(2(1+x))$

Expansion of g.f. (1- sqrt 1-4x-4x^2 )/(2(1+x))

Formal Conjectures· Specialist source · status unassessed

OP-9880Number theoryStatus unassessed

Apéry numbers

Formal Conjectures· Specialist source · status unassessed

OP-9879Number theoryStatus unassessed

Maximum exponent in the prime factorization of $n$

Maximum exponent in the prime factorization of n

Formal Conjectures· Specialist source · status unassessed

OP-9878Number theoryStatus unassessed

Practical numbers

Formal Conjectures· Specialist source · status unassessed

OP-9877Number theoryStatus unassessed

Nearest integer to $n/\sqrt{2}$

Nearest integer to n/ sqrt 2

Formal Conjectures· Specialist source · status unassessed

OP-9876Number theoryStatus unassessed

$a(n) = \sum_{k=1}^n (k^2 \bmod n)$

a(n) = sum k=1 ^n (k^2 bmod n)

Formal Conjectures· Specialist source · status unassessed

OP-9875Number theoryStatus unassessed

Denominators of coefficients in Stirling's expansion for $\log(\Gamma(z))$

Denominators of coefficients in Stirling's expansion for log( Gamma(z))

Formal Conjectures· Specialist source · status unassessed

OP-9874Number theoryStatus unassessed

Least positive multiple of $n$ in base 10 with digits 0 and 1

Least positive multiple of n in base 10 with digits 0 and 1

Formal Conjectures· Specialist source · status unassessed

OP-9873Number theoryStatus unassessed

No powers as partition numbers

Formal Conjectures· Specialist source · status unassessed

OP-9872Number theoryStatus unassessed

The prime numbers

Formal Conjectures· Specialist source · status unassessed

OP-9871Number theoryStatus unassessed

Smallest composite $c$ such that $\textrm{primorial}(n) + c$ is prime

Smallest composite c such that textrm primorial (n) + c is prime

Formal Conjectures· Specialist source · status unassessed

OP-9870Number theoryStatus unassessed

Conjectures associated with A038552

Formal Conjectures· Specialist source · status unassessed

OP-9869Number theoryStatus unassessed

Number of primes $< n^2$

Number of primes < n^2

Formal Conjectures· Specialist source · status unassessed

OP-9868Number theoryStatus unassessed

Number of primes $< n^3$

Number of primes < n^3

Formal Conjectures· Specialist source · status unassessed

OP-9867Number theoryStatus unassessed

Home primes (OEIS A037274)

Formal Conjectures· Specialist source · status unassessed

OP-9866Number theoryStatus unassessed

Numerator of a sum involving binomial coefficients

Formal Conjectures· Specialist source · status unassessed

OP-9865Number theoryStatus unassessed

Smallest prime $\equiv 1 \pmod n$

Smallest prime equiv 1 pmod n

Formal Conjectures· Specialist source · status unassessed

OP-9864Number theoryStatus unassessed

Smallest number $k$ such that $kn + 1$ is prime

Smallest number k such that kn + 1 is prime

Formal Conjectures· Specialist source · status unassessed

OP-9863Number theoryStatus unassessed

Concatenation of the next nnn numbers

a(n)=(smallest prime>n2)−n2a(n) = (\text{smallest prime} > n^2) - n^2a(n)=(smallest prime>n2)−n2

Expansion of g.f. (1−1−4x−4x2)/(2(1+x))(1-\sqrt{1-4x-4x^2})/(2(1+x))(1−1−4x−4x2​)/(2(1+x))

Apéry numbers

Maximum exponent in the prime factorization of nnn

Practical numbers

Nearest integer to n/2n/\sqrt{2}n/2​

a(n)=∑k=1n(k2 mod n)a(n) = \sum_{k=1}^n (k^2 \bmod n)a(n)=∑k=1n​(k2modn)

Denominators of coefficients in Stirling's expansion for log⁡(Γ(z))\log(\Gamma(z))log(Γ(z))

Least positive multiple of nnn in base 10 with digits 0 and 1

No powers as partition numbers

The prime numbers

Smallest composite ccc such that primorial(n)+c\textrm{primorial}(n) + cprimorial(n)+c is prime

Conjectures associated with A038552

Number of primes <n2< n^2<n2

Number of primes <n3< n^3<n3

Home primes (OEIS A037274)

Numerator of a sum involving binomial coefficients

Smallest prime ≡1(modn)\equiv 1 \pmod n≡1(modn)

Smallest number kkk such that kn+1kn + 1kn+1 is prime

A binomial coefficient summation

A binomial coefficient sum

Four-square conjecture with powers of 2, 3, and 5

The 2-4-6-8 Conjecture

Sum of two squares, a power of 3, and a power of 5

Concatenation of the next $n$ numbers

$a(n) = (\text{smallest prime} > n^2) - n^2$

Expansion of g.f. $(1-\sqrt{1-4x-4x^2})/(2(1+x))$

Maximum exponent in the prime factorization of $n$

Nearest integer to $n/\sqrt{2}$

$a(n) = \sum_{k=1}^n (k^2 \bmod n)$

Denominators of coefficients in Stirling's expansion for $\log(\Gamma(z))$

Least positive multiple of $n$ in base 10 with digits 0 and 1

Smallest composite $c$ such that $\textrm{primorial}(n) + c$ is prime

Number of primes $< n^2$

Number of primes $< n^3$

Smallest prime $\equiv 1 \pmod n$

Smallest number $k$ such that $kn + 1$ is prime