Problems · OpenFrontiers

OP-9783Number theoryStatus unassessed

Numbers $n$ such that the perfect deficiency of $n$ is $\le 10$ .

Numbers n such that the perfect deficiency of n is le 10 .

Formal Conjectures· Specialist source · status unassessed

OP-9782Number theoryStatus unassessed

Numbers $n$ such that $\phi(n) = \phi(n + \phi(n))$

Numbers n such that phi(n) = phi(n + phi(n))

Formal Conjectures· Specialist source · status unassessed

OP-9781Number theoryStatus unassessed

Digital sum of the Fermat number $2^{2^n} + 1$

Digital sum of the Fermat number 2^ 2^n + 1

Formal Conjectures· Specialist source · status unassessed

OP-9780Number theoryStatus unassessed

Riesel Problem

Formal Conjectures· Specialist source · status unassessed

OP-9779CombinatoricsStatus unassessed

$a(n) = \sum_{i=0}^n \binom{2n-i}{n+i}$

a(n) = sum i=0 ^n binom 2n-i n+i

Formal Conjectures· Specialist source · status unassessed

OP-9778Number theoryStatus unassessed

Sum of squares of nonacci numbers

Formal Conjectures· Specialist source · status unassessed

OP-9777Number theoryStatus unassessed

Imaginary part of $\prod_{k=0}^n (1 + k \cdot i)$ , $i = \sqrt{-1}$

Imaginary part of prod k=0 ^n (1 + k cdot i) , i = sqrt -1

Formal Conjectures· Specialist source · status unassessed

OP-9776Number theoryStatus unassessed

Number of zeros in ternary representation of $2^n$

Number of zeros in ternary representation of 2^n

Formal Conjectures· Specialist source · status unassessed

OP-9772Number theoryStatus unassessed

$a(n) = [x^{2n}] \left(\frac{1 + x}{1 - x}\right)^n$

a(n) = [x^ 2n ] left( frac 1 + x 1 - x right)^n

Formal Conjectures· Specialist source · status unassessed

OP-9771Number theoryStatus unassessed

Smallest power with base>1 and exponent $n$ without digit 0

Smallest power with base 1 and exponent n without digit 0

Formal Conjectures· Specialist source · status unassessed

OP-9770Number theoryStatus unassessed

$a(n) = 3a(n-1) + a(n-2) - 3a(n-3)$

a(n) = 3a(n-1) + a(n-2) - 3a(n-3)

Formal Conjectures· Specialist source · status unassessed

OP-9769Number theoryStatus unassessed

Number of decompositions of $2n+1$ into $2p+q$ , where $p$ and $q$ are both odd primes

Number of decompositions of 2n+1 into 2p+q , where p and q are both odd primes

Formal Conjectures· Specialist source · status unassessed

OP-9768Number theoryStatus unassessed

$a(0) = 1$ , $a(n) = a(n-1)a(n-1) + 2$

a(0) = 1 , a(n) = a(n-1)a(n-1) + 2

Formal Conjectures· Specialist source · status unassessed

OP-9767Number theoryStatus unassessed

Conjectures associated with A101779

Formal Conjectures· Specialist source · status unassessed

OP-9766Number theoryStatus unassessed

Conjectures associated with A100800

Formal Conjectures· Specialist source · status unassessed

OP-9765Number theoryStatus unassessed

Prime-th recurrence with reversal at each step

Formal Conjectures· Specialist source · status unassessed

OP-9764Number theoryStatus unassessed

Conjectures associated with A100474

Formal Conjectures· Specialist source · status unassessed

OP-9763Number theoryStatus unassessed

Riemann Hypothesis and its generalizations

Formal Conjectures· Specialist source · status unassessed

OP-9762Computational complexityStatus unassessed

Conjectures in Complexity Theory

Formal Conjectures· Specialist source · status unassessed

OP-9761Geometry and topologyStatus unassessed

Poincare

Formal Conjectures· Specialist source · status unassessed

OP-9760Partial differential equationsStatus unassessed

Existence And Smoothness Of The Navier–Stokes Equation

Formal Conjectures· Specialist source · status unassessed

OP-9759Number theoryStatus unassessed

The Birch and Swinnerton-Dyer (BSD) Conjecture

Formal Conjectures· Specialist source · status unassessed

Numbers nnn such that the perfect deficiency of nnn is ≤10\le 10≤10.

Numbers nnn such that ϕ(n)=ϕ(n+ϕ(n))\phi(n) = \phi(n + \phi(n))ϕ(n)=ϕ(n+ϕ(n))

Digital sum of the Fermat number 22n+12^{2^n} + 122n+1

Riesel Problem

a(n)=∑i=0n(2n−in+i)a(n) = \sum_{i=0}^n \binom{2n-i}{n+i}a(n)=∑i=0n​(n+i2n−i​)

Sum of squares of nonacci numbers

Imaginary part of ∏k=0n(1+k⋅i)\prod_{k=0}^n (1 + k \cdot i)∏k=0n​(1+k⋅i), i=−1i = \sqrt{-1}i=−1​

Triangular matchstick numbers in the class of prime numbers

Conjectures associated with A105210

Array read by upward antidiagonals

Number of zeros in ternary representation of 2n2^n2n

a(n)=[x2n](1+x1−x)na(n) = [x^{2n}] \left(\frac{1 + x}{1 - x}\right)^na(n)=[x2n](1−x1+x​)n

Smallest power with base>1 and exponent nnn without digit 0

a(n)=3a(n−1)+a(n−2)−3a(n−3)a(n) = 3a(n-1) + a(n-2) - 3a(n-3)a(n)=3a(n−1)+a(n−2)−3a(n−3)

Number of decompositions of 2n+12n+12n+1 into 2p+q2p+q2p+q, where ppp and qqq are both odd primes

a(0)=1a(0) = 1a(0)=1, a(n)=a(n−1)a(n−1)+2a(n) = a(n-1)a(n-1) + 2a(n)=a(n−1)a(n−1)+2

Conjectures associated with A101779

Conjectures associated with A100800

Prime-th recurrence with reversal at each step

Conjectures associated with A100474

Riemann Hypothesis and its generalizations

Conjectures in Complexity Theory

Poincare

Existence And Smoothness Of The Navier–Stokes Equation

The Birch and Swinnerton-Dyer (BSD) Conjecture

Numbers $n$ such that the perfect deficiency of $n$ is $\le 10$ .

Numbers $n$ such that $\phi(n) = \phi(n + \phi(n))$

Digital sum of the Fermat number $2^{2^n} + 1$

$a(n) = \sum_{i=0}^n \binom{2n-i}{n+i}$

Imaginary part of $\prod_{k=0}^n (1 + k \cdot i)$ , $i = \sqrt{-1}$

Number of zeros in ternary representation of $2^n$

$a(n) = [x^{2n}] \left(\frac{1 + x}{1 - x}\right)^n$

Smallest power with base>1 and exponent $n$ without digit 0

$a(n) = 3a(n-1) + a(n-2) - 3a(n-3)$

Number of decompositions of $2n+1$ into $2p+q$ , where $p$ and $q$ are both odd primes

$a(0) = 1$ , $a(n) = a(n-1)a(n-1) + 2$