Problems · OpenFrontiers

OP-9808Number theoryStatus unassessed

Partial sums of $\binom{2n}{n}^2$

Partial sums of binom 2n n ^2

Formal Conjectures· Specialist source · status unassessed

OP-9807Number theoryStatus unassessed

$a(n) = 2^(2^n)$

a(n) = 2^(2^n)

Formal Conjectures· Specialist source · status unassessed

OP-9806Number theoryStatus unassessed

Numerator of $\zeta(4n)/\zeta(2n)^2$ (with $a(0)=2$ instead of $-2$ )

Numerator of zeta(4n)/ zeta(2n)^2 (with a(0)=2 instead of -2 )

Formal Conjectures· Specialist source · status unassessed

OP-9805Number theoryStatus unassessed

Largest odd divisor of $a(n-1) + \textrm{prime}(n)$

Largest odd divisor of a(n-1) + textrm prime (n)

Formal Conjectures· Specialist source · status unassessed

OP-9804Number theoryStatus unassessed

Difference between first odd semiprime $> 2^n$ and $2^n$

Difference between first odd semiprime 2^n and 2^n

Formal Conjectures· Specialist source · status unassessed

OP-9803Number theoryStatus unassessed

Number of prime powers $q<=n$ such that also $q+2$ is a prime power

Number of prime powers q<=n such that also q+2 is a prime power

Formal Conjectures· Specialist source · status unassessed

OP-9802Number theoryStatus unassessed

Ascending descending base exponent transform of $2^n$

Ascending descending base exponent transform of 2^n

Formal Conjectures· Specialist source · status unassessed

OP-9801Number theoryStatus unassessed

Ascending descending base exponent transform of factorials

Formal Conjectures· Specialist source · status unassessed

OP-9800Number theoryStatus unassessed

Ascending descending base exponent transform of squares

Formal Conjectures· Specialist source · status unassessed

OP-9799Number theoryStatus unassessed

Smallest number $m$ such that $2^n - m$ and $2^n + m$ are primes

Smallest number m such that 2^n - m and 2^n + m are primes

Formal Conjectures· Specialist source · status unassessed

OP-9798Number theoryStatus unassessed

Number of digits of n raised to the power of the sum of the digits of n

Formal Conjectures· Specialist source · status unassessed

OP-9797Number theoryStatus unassessed

Number of refactorable numbers (A033950) $\le 10^n$

Number of refactorable numbers (A033950) le 10^n

Formal Conjectures· Specialist source · status unassessed

OP-9796Number theoryStatus unassessed

Integer part of $\mathrm{prime}(n)/\pi(n)$

Integer part of mathrm prime (n)/ pi(n)

Formal Conjectures· Specialist source · status unassessed

OP-9795Number theoryStatus unassessed

Conjectures associated with A110854

Formal Conjectures· Specialist source · status unassessed

OP-9794Number theoryStatus unassessed

Smallest $m > 0$ such that there are no primes between $nm$ and $n(m+1)$ inclusive.

Smallest m 0 such that there are no primes between nm and n(m+1) inclusive.

Formal Conjectures· Specialist source · status unassessed

OP-9793Number theoryStatus unassessed

$a(n) = \operatorname{lcm}\{1,2,\dots,n\}/\operatorname{denom}(H(n))$

a(n) = operatorname lcm 1,2, dots,n / operatorname denom (H(n))

Formal Conjectures· Specialist source · status unassessed

OP-9792Number theoryStatus unassessed

Number of symbols '*' and '^' to write the canonical prime factorization of n

Number of symbols ' ' and '^' to write the canonical prime factorization of n

Formal Conjectures· Specialist source · status unassessed

OP-9791Number theoryStatus unassessed

Numerator of $\binom{6n-2}{2n} / \left(2 \binom{4n-1}{2n}\right)$

Numerator of binom 6n-2 2n / left(2 binom 4n-1 2n right)

Formal Conjectures· Specialist source · status unassessed

OP-9784Number theoryStatus unassessed

Numerator of $\sum_{k=1}^n 2^k/k$ .

Numerator of sum k=1 ^n 2^k/k .

Formal Conjectures· Specialist source · status unassessed

Partial sums of (2nn)2\binom{2n}{n}^2(n2n​)2

a(n)=2(2n)a(n) = 2^(2^n)a(n)=2(2n)

Numerator of ζ(4n)/ζ(2n)2\zeta(4n)/\zeta(2n)^2ζ(4n)/ζ(2n)2 (with a(0)=2a(0)=2a(0)=2 instead of −2-2−2)

Largest odd divisor of a(n−1)+prime(n)a(n-1) + \textrm{prime}(n)a(n−1)+prime(n)

Difference between first odd semiprime >2n> 2^n>2n and 2n2^n2n

Number of prime powers q<=nq<=nq<=n such that also q+2q+2q+2 is a prime power

Ascending descending base exponent transform of 2n2^n2n

Ascending descending base exponent transform of factorials

Ascending descending base exponent transform of squares

Smallest number mmm such that 2n−m2^n - m2n−m and 2n+m2^n + m2n+m are primes

Number of digits of n raised to the power of the sum of the digits of n

Number of refactorable numbers (A033950) ≤10n\le 10^n≤10n

Integer part of prime(n)/π(n)\mathrm{prime}(n)/\pi(n)prime(n)/π(n)

Conjectures associated with A110854

Smallest m>0m > 0m>0 such that there are no primes between nmnmnm and n(m+1)n(m+1)n(m+1) inclusive.

a(n)=lcm⁡{1,2,…,n}/denom⁡(H(n))a(n) = \operatorname{lcm}\{1,2,\dots,n\}/\operatorname{denom}(H(n))a(n)=lcm{1,2,…,n}/denom(H(n))

Number of symbols '*' and '^' to write the canonical prime factorization of n

Conjectures associated with A109909

Conjectures associated with A109908

Conjectures associated with A109905

Conjectures associated with A109845

Conjectures associated with A109671

Conjectures associated with A109227

Numerator of (6n−22n)/(2(4n−12n))\binom{6n-2}{2n} / \left(2 \binom{4n-1}{2n}\right)(2n6n−2​)/(2(2n4n−1​))

Numerator of ∑k=1n2k/k\sum_{k=1}^n 2^k/k∑k=1n​2k/k.

Partial sums of $\binom{2n}{n}^2$

$a(n) = 2^(2^n)$

Numerator of $\zeta(4n)/\zeta(2n)^2$ (with $a(0)=2$ instead of $-2$ )

Largest odd divisor of $a(n-1) + \textrm{prime}(n)$

Difference between first odd semiprime $> 2^n$ and $2^n$

Number of prime powers $q<=n$ such that also $q+2$ is a prime power

Ascending descending base exponent transform of $2^n$

Smallest number $m$ such that $2^n - m$ and $2^n + m$ are primes

Number of refactorable numbers (A033950) $\le 10^n$

Integer part of $\mathrm{prime}(n)/\pi(n)$

Smallest $m > 0$ such that there are no primes between $nm$ and $n(m+1)$ inclusive.

$a(n) = \operatorname{lcm}\{1,2,\dots,n\}/\operatorname{denom}(H(n))$

Numerator of $\binom{6n-2}{2n} / \left(2 \binom{4n-1}{2n}\right)$

Numerator of $\sum_{k=1}^n 2^k/k$ .