List questions from experimental-mathematics

Published on 16 Mar 2026 - 20:41

20

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Prove the following property for the given sequence.

Published on 17 Mar 2026 - 10:57

82

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Let $x(n)=$ product of first $n$ primes.How often is $x(n)$ triangular?

Published on 17 Mar 2026 - 22:45

73

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Hubs in high-dimensional point clouds (distribution of "being within nearest neighbours of how_many other points")

Published on 21 Nov 2018 - 10:21

568

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What is probability that: (a)a non leap year has 53 Sundays. (b)a leap year has 53 fridays.

Published on 01 Jan 2019 - 17:07

254

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Modified Pascal's triangle

Published on 16 Mar 2026 - 22:35

636

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Digits of $\pi$ in other bases?

Published on 16 Mar 2026 - 22:25

407

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Figures and Numbers: Relating properties of geometric shapes and their Fourier series

Published on 05 Apr 2019 - 12:42

291

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The number $\pi$ in an unexpected context

Published on 17 Mar 2026 - 4:30

566

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On binomial sums $\sum_{n=1}^\infty \frac{1}{n^k\,\binom {2n}n}$ and log sine integrals

Published on 04 May 2019 - 6:26

30

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Understanding "Comparison" method in statistics

Published on 17 Mar 2026 - 4:52

291

Views

Semiperimeter of isosceles Heronian triangles.

Published on 17 Mar 2026 - 12:16

230

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An asymptotic series for $\small\prod_{k=n}^\infty\operatorname{sinc}\left({2^{-k}}\pi\right),\,n\to\infty$

Published on 27 May 2019 - 14:50

696

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Prove that $\int_0^\infty\left(\arctan \frac1x\right)^2 \mathrm d x = \pi\ln 2$

Published on 07 Jun 2019 - 15:24

289

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Is there an identity between the Clausen function $\rm{Cl}_8\left(\frac\pi3\right)$ and $\sum_{n=1}^\infty \frac{1}{n^9\,\binom {2n}n}$?

Published on 10 Jun 2019 - 5:25

List Question

About Utterly odd numbers.

Prove the following property for the given sequence.

Let $x(n)=$ product of first $n$ primes.How often is $x(n)$ triangular?

Hubs in high-dimensional point clouds (distribution of "being within nearest neighbours of how_many other points")

What is probability that: (a)a non leap year has 53 Sundays. (b)a leap year has 53 fridays.

Modified Pascal's triangle

Digits of $\pi$ in other bases?

Figures and Numbers: Relating properties of geometric shapes and their Fourier series

The number $\pi$ in an unexpected context

On binomial sums $\sum_{n=1}^\infty \frac{1}{n^k\,\binom {2n}n}$ and log sine integrals

Understanding "Comparison" method in statistics

Semiperimeter of isosceles Heronian triangles.

An asymptotic series for $\small\prod_{k=n}^\infty\operatorname{sinc}\left({2^{-k}}\pi\right),\,n\to\infty$

Prove that $\int_0^\infty\left(\arctan \frac1x\right)^2 \mathrm d x = \pi\ln 2$

Is there an identity between the Clausen function $\rm{Cl}_8\left(\frac\pi3\right)$ and $\sum_{n=1}^\infty \frac{1}{n^9\,\binom {2n}n}$?

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