User Vincent Granville - Mathematics Stack Exchange

46 votes

1 answer

2k views

Limit associated with a recursion

asked Aug 17, 2019 at 17:31

22 votes

3 answers

998 views

Derivative and calculus over sets such as the rational numbers

asked Dec 6, 2019 at 14:53

20 votes

2 answers

608 views

Simple recurrences converging to $\log 2, \pi, e, \sqrt{2}$ and so on

asked Dec 29, 2019 at 19:12

18 votes

1 answer

614 views

A simple irrational number with the same first 11,667,755 digits as $\frac{2}{3}$

asked Sep 2, 2019 at 4:21

17 votes

3 answers

993 views

Potentially new approach to factoring big numbers

asked May 11, 2020 at 8:34

15 votes

2 answers

527 views

Successive records in mathematical sequences: surprising result

asked Aug 27, 2019 at 16:36

13 votes

1 answer

364 views

The proportion of binary digits of $\sum_{k=1}^\infty \Big\lfloor{\frac{k}{2}\sqrt{p}\Big\rfloor}\cdot2^{-k}$ equal to one, is $> 0.978$ if $p=143$.

asked Dec 22, 2019 at 20:11

13 votes

0 answers

257 views

Asymptotic behavior of recurrence $x_{n+1}=\mbox{Stdev}(x_1,\dots,x_n)$

asked Jul 4, 2021 at 22:30

11 votes

1 answer

374 views

If an infinite set $S$ of positive integers is equidistributed, is $S+S$ also equidistributed?

asked Jul 16, 2020 at 1:00

11 votes

1 answer

589 views

Towards a Little proof of Fermat's last theorem

asked Dec 26, 2019 at 18:07

11 votes

1 answer

259 views

Strange approximation to $\sqrt{\pi}$

asked Oct 24, 2019 at 14:32

10 votes

1 answer

421 views

Which positive continuous functions satisfy $F(x) = F(e^x)-F(e^{-x})$ for $x\geq 0$?

asked May 29, 2019 at 19:35

9 votes

3 answers

440 views

On sums such as $\sum_{k=0}^\infty \binom{2k}{k}\frac{1}{8^k}=\sqrt{2}$

asked Dec 27, 2019 at 17:19

9 votes

2 answers

406 views

Question about $f(x)=\sum_{k=1}^\infty (-1)^{k+1}\sin (\frac{x}{k}) $

asked Apr 12, 2020 at 19:54

8 votes

2 answers

760 views

Conjecture: All but 21 non-square integers are the sum of a square and a prime

asked Jun 7, 2020 at 18:51

8 votes

0 answers

434 views

New numeration system, mapping to binary numeration system

asked Dec 15, 2019 at 21:01

7 votes

3 answers

427 views

Non standard solution to $f(x) = \frac{1}{2}\Big(f(\frac{x}{2}) + f(\frac{1+x}{2})\Big)$

asked Aug 21, 2019 at 16:50

6 votes

1 answer

105 views

Need any kind of insights about a strange function

asked Jul 26, 2019 at 21:27

6 votes

2 answers

490 views

Integral $\int_0^\infty \frac{|\sin\sqrt{qx}|-|\sin\sqrt{px}|}{x}dx$

asked Apr 9, 2019 at 1:59

6 votes

0 answers

213 views

Enhanced Berry-Esseen theorem for the digits of $\sqrt{2}$

asked Aug 26, 2019 at 17:05

6 votes

0 answers

186 views

About solving $f(z) = \frac{1}{4} (f(-1-z) +2 f(-1-2z)+ 2f(-1+2z) +f(-1+z))$

asked Nov 12, 2019 at 5:46

5 votes

1 answer

169 views

Taylor series for $\sqrt{x^0+\sqrt{x^1+\sqrt{x^2+\cdots}}}$

asked Oct 24, 2019 at 17:37

5 votes

2 answers

626 views

Limit associated with a recursion, connection to normality of quadratic irrationals

asked Feb 7, 2020 at 7:46

4 votes

1 answer

192 views

Simple recursion or closed form for $\lfloor 2^n \sqrt{2}\rfloor$

asked Sep 18, 2019 at 15:32

4 votes

1 answer

373 views

Twin Primes Conjecture and related problems

asked Sep 29, 2019 at 0:42

4 votes

0 answers

156 views

Is the rabbit constant the first natural math constant found to be non-normal?

asked Apr 27, 2019 at 21:25

4 votes

2 answers

86 views

An intriguing recursion

asked Aug 6, 2019 at 20:37

4 votes

2 answers

403 views

Maximum run in binary digit expansions

asked Aug 10, 2019 at 15:23

3 votes

1 answer

96 views

Spectacular approximation to $\sum_{k=1}^n \{k \log_2 3\}$ where the curly brackets represent the fractional part

asked Aug 2, 2019 at 23:39

3 votes

1 answer

72 views

Some distributions / auto-correlations associated with irrational numbers

asked Aug 14, 2019 at 17:19

Stack Exchange Network

88 Questions

Limit associated with a recursion

Derivative and calculus over sets such as the rational numbers

Simple recurrences converging to $\log 2, \pi, e, \sqrt{2}$ and so on

A simple irrational number with the same first 11,667,755 digits as $\frac{2}{3}$

Potentially new approach to factoring big numbers

Successive records in mathematical sequences: surprising result

The proportion of binary digits of $\sum_{k=1}^\infty \Big\lfloor{\frac{k}{2}\sqrt{p}\Big\rfloor}\cdot2^{-k}$ equal to one, is $> 0.978$ if $p=143$.

Asymptotic behavior of recurrence $x_{n+1}=\mbox{Stdev}(x_1,\dots,x_n)$

If an infinite set $S$ of positive integers is equidistributed, is $S+S$ also equidistributed?

Towards a Little proof of Fermat's last theorem

Strange approximation to $\sqrt{\pi}$

Which positive continuous functions satisfy $F(x) = F(e^x)-F(e^{-x})$ for $x\geq 0$?

On sums such as $\sum_{k=0}^\infty \binom{2k}{k}\frac{1}{8^k}=\sqrt{2}$

Question about $f(x)=\sum_{k=1}^\infty (-1)^{k+1}\sin (\frac{x}{k}) $

Conjecture: All but 21 non-square integers are the sum of a square and a prime

New numeration system, mapping to binary numeration system

Non standard solution to $f(x) = \frac{1}{2}\Big(f(\frac{x}{2}) + f(\frac{1+x}{2})\Big)$

Need any kind of insights about a strange function

Integral $\int_0^\infty \frac{|\sin\sqrt{qx}|-|\sin\sqrt{px}|}{x}dx$

Enhanced Berry-Esseen theorem for the digits of $\sqrt{2}$

About solving $f(z) = \frac{1}{4} (f(-1-z) +2 f(-1-2z)+ 2f(-1+2z) +f(-1+z))$

Taylor series for $\sqrt{x^0+\sqrt{x^1+\sqrt{x^2+\cdots}}}$

Limit associated with a recursion, connection to normality of quadratic irrationals

Simple recursion or closed form for $\lfloor 2^n \sqrt{2}\rfloor$

Twin Primes Conjecture and related problems

Is the rabbit constant the first natural math constant found to be non-normal?

An intriguing recursion

Maximum run in binary digit expansions

Spectacular approximation to $\sum_{k=1}^n \{k \log_2 3\}$ where the curly brackets represent the fractional part

Some distributions / auto-correlations associated with irrational numbers