Problems · OpenFrontiers

OP-9858Number theoryStatus unassessed

Sum of a triangular number, a generalized pentagonal number, and a generalized heptagonal number

Formal Conjectures· Specialist source · status unassessed

OP-9857Number theoryStatus unassessed

Central factorial numbers: $((2n)!!)^2$

Central factorial numbers: ((2n)!!)^2

Formal Conjectures· Specialist source · status unassessed

OP-9853Number theoryStatus unassessed

Determinant of Hankel matrix of the first $2n-1$ prime numbers

Determinant of Hankel matrix of the first 2n-1 prime numbers

Formal Conjectures· Specialist source · status unassessed

OP-9852Number theoryStatus unassessed

Central trinomial coefficients

Formal Conjectures· Specialist source · status unassessed

OP-9851Number theoryStatus unassessed

Cuban Primes

Formal Conjectures· Specialist source · status unassessed

OP-9850Number theoryStatus unassessed

Number of parts in the symmetric representation of $\sigma(n)$

Number of parts in the symmetric representation of sigma(n)

Formal Conjectures· Specialist source · status unassessed

OP-9849Number theoryStatus unassessed

Multiplicative order of 2 mod $2n+1$

Multiplicative order of 2 mod 2n+1

Formal Conjectures· Specialist source · status unassessed

OP-9848Number theoryStatus unassessed

Representations with prime conditions

Formal Conjectures· Specialist source · status unassessed

OP-9847Number theoryStatus unassessed

Sum of two numbers with prime conditions

Formal Conjectures· Specialist source · status unassessed

OP-9846Number theoryStatus unassessed

Numbers $n$ such that $n^2 + \pi(n)$ is prime

Numbers n such that n^2 + pi(n) is prime

Formal Conjectures· Specialist source · status unassessed

OP-9845Number theoryStatus unassessed

Number of squares $\bmod n$

Number of squares bmod n

Formal Conjectures· Specialist source · status unassessed

OP-9844Number theoryStatus unassessed

A nonlinear recurrence sequence

Formal Conjectures· Specialist source · status unassessed

OP-9843Number theoryStatus unassessed

Integrality and supercongruences of the factorial ratio $\frac{(6n)! n!}{(3n)! (2n)!^2}$

Integrality and supercongruences of the factorial ratio frac (6n)! n! (3n)! (2n)!^2

Formal Conjectures· Specialist source · status unassessed

OP-9842Number theoryStatus unassessed

Coefficients of $\prod_{k>0} (1 - x^k/k!)$

Coefficients of prod k 0 (1 - x^k/k!)

Formal Conjectures· Specialist source · status unassessed

OP-9841Number theoryStatus unassessed

Number of odd primes between $n^2$ and $(n+1)^2$ with $(n/p) = 1$

Number of odd primes between n^2 and (n+1)^2 with (n/p) = 1

Formal Conjectures· Specialist source · status unassessed

OP-9840Number theoryStatus unassessed

Recurrence with bitwise XOR

Formal Conjectures· Specialist source · status unassessed

OP-9839Number theoryStatus unassessed

Product of two consecutive primes modulo the next prime

Formal Conjectures· Specialist source · status unassessed

OP-9838Number theoryStatus unassessed

Squares of double factorials

Formal Conjectures· Specialist source · status unassessed

OP-9837Number theoryStatus unassessed

Sum of fourth powers of Fibonacci-like binomial coefficients

Formal Conjectures· Specialist source · status unassessed

OP-9836Number theoryStatus unassessed

Difference of digit sums in base 3 and base 2

Formal Conjectures· Specialist source · status unassessed

OP-9835Number theoryStatus unassessed

Central binomial sum $a(n) = \sum_{k=0}^n \binom{n}{k}^2 \binom{n-k}{k}^2 (-16)^k$

Central binomial sum a(n) = sum k=0 ^n binom n k ^2 binom n-k k ^2 (-16)^k

Formal Conjectures· Specialist source · status unassessed

OP-9834Number theoryStatus unassessed

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 (-4)^k binom n k ^2 binom n-k k ^2

Formal Conjectures· Specialist source · status unassessed

Sum of a triangular number, a generalized pentagonal number, and a generalized heptagonal number

Sum of four squares with square conditions

The 1680-Conjecture

A GCD-Driven Sequence with Universal Jumps

Central factorial numbers: ((2n)!!)2((2n)!!)^2((2n)!!)2

Determinant of Hankel matrix of the first 2n−12n-12n−1 prime numbers

Central trinomial coefficients

Cuban Primes

Number of parts in the symmetric representation of σ(n)\sigma(n)σ(n)

Multiplicative order of 2 mod 2n+12n+12n+1

Representations with prime conditions

Sum of two numbers with prime conditions

Numbers nnn such that n2+π(n)n^2 + \pi(n)n2+π(n) is prime

Number of squares mod n\bmod nmodn

A nonlinear recurrence sequence

Integrality and supercongruences of the factorial ratio (6n)!n!(3n)!(2n)!2\frac{(6n)! n!}{(3n)! (2n)!^2}(3n)!(2n)!2(6n)!n!​

Coefficients of ∏k>0(1−xk/k!)\prod_{k>0} (1 - x^k/k!)∏k>0​(1−xk/k!)

Number of odd primes between n2n^2n2 and (n+1)2(n+1)^2(n+1)2 with (n/p)=1(n/p) = 1(n/p)=1

Recurrence with bitwise XOR

Product of two consecutive primes modulo the next prime

Squares of double factorials

Sum of fourth powers of Fibonacci-like binomial coefficients

Difference of digit sums in base 3 and base 2

Central binomial sum a(n)=∑k=0n(nk)2(n−kk)2(−16)ka(n) = \sum_{k=0}^n \binom{n}{k}^2 \binom{n-k}{k}^2 (-16)^ka(n)=∑k=0n​(kn​)2(kn−k​)2(−16)k

Central binomial sum a(n)=∑k=0n(−4)k(nk)2(n−kk)2a(n) = \sum_{k=0}^n (-4)^k \binom{n}{k}^2 \binom{n-k}{k}^2a(n)=∑k=0n​(−4)k(kn​)2(kn−k​)2

Central factorial numbers: $((2n)!!)^2$

Determinant of Hankel matrix of the first $2n-1$ prime numbers

Number of parts in the symmetric representation of $\sigma(n)$

Multiplicative order of 2 mod $2n+1$

Numbers $n$ such that $n^2 + \pi(n)$ is prime

Number of squares $\bmod n$

Integrality and supercongruences of the factorial ratio $\frac{(6n)! n!}{(3n)! (2n)!^2}$

Coefficients of $\prod_{k>0} (1 - x^k/k!)$

Number of odd primes between $n^2$ and $(n+1)^2$ with $(n/p) = 1$

Central binomial sum $a(n) = \sum_{k=0}^n \binom{n}{k}^2 \binom{n-k}{k}^2 (-16)^k$

Central binomial sum $a(n) = \sum_{k=0}^n (-4)^k \binom{n}{k}^2 \binom{n-k}{k}^2$