Question

how to find number of presentation of 1 as a sum of $2^{-i}$?

score 104 · Answer 1 · 2023-03-26 14:27:28

104

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how to find number of presentation of 1 as a sum of $2^{-i}$?

Published on 26 Mar 2023 - 14:27

score 107 · Answer 2 · 2023-04-22 18:27:03

107

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The longest sequence of unique unit fractions that sums to 1, given a specific bound on the denominators

Published on 22 Apr 2023 - 18:27

score 81 · Answer 3 · 2023-04-25 11:26:07

81

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$A = \sum_{i=1}^{\infty} \frac{i}{a_i}$ and $1 = \sum_{i=1}^{\infty} \frac{1}{a_i}$?

Published on 25 Apr 2023 - 11:26

score 99 · Answer 4 · 2023-05-13 16:18:01

99

Views

Reference Request - Online copy of R. Graham's "On Finite Sums of Rational Numbers"

Published on 13 May 2023 - 16:18

score 475 · Answer 5 · 2023-08-23 18:45:22

475

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Is there a finite set of distinct naturals whose reciprocals sum to 1, and no element in the set is one less than a prime?

Published on 23 Aug 2023 - 18:45

score 95 · Answer 6 · 2023-10-01 14:23:48

95

Views

What is known about the average growth rate of the denominators of $n$ Egyptian fractions summing to one?

Published on 01 Oct 2023 - 14:23

score 38 · Answer 7 · 2023-10-19 15:57:34

38

Views

Four different positive integers whose reciprocals sum to 1

Published on 19 Oct 2023 - 15:57

score 34 · Answer 8 · 2023-10-27 02:14:58

34

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Expressing one as a sum of unique unit fractions whose denominators are increasing?

Published on 27 Oct 2023 - 2:14

score 96 · Answer 9 · 2023-10-27 15:28:26

96

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Have the prime Egyptian fractionary expansions of rational numbers been studied before?

Published on 27 Oct 2023 - 15:28

score 80 · Answer 10 · 2023-10-29 10:36:39

80

Views

Egyptian fraction of length 3 in the interval (0.5,1)

Published on 29 Oct 2023 - 10:36

score 57 · Answer 11 · 2023-10-29 18:00:44

57

Views

Egyptian fraction of a number in the interval (0.5,1)

Published on 29 Oct 2023 - 18:00

score 234 · Answer 12 · 2023-11-05 14:05:00

234

Views

Has the diophantine equation $ \sum_{n=1}^{N} \frac{1}{x_{n}} = \prod_{k=1}^{N} \left(1-\frac{1}{x_{k}} \right) $ been studied?

Published on 05 Nov 2023 - 14:05

score 349 · Answer 13 · 2023-12-06 23:49:27

349

Views

Conjecture: If $\sum_{i=1}^n \frac{1}{x_i}=1$ then $x_i | x_j$

Published on 06 Dec 2023 - 23:49

score 76 · Answer 14 · 2024-01-30 08:43:34

76

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$m_i, n_j$ integers and $\{m_i\}_{i=1}^{k}\neq\{n_j\}_{j=1}^{k'}.$ Does $\sum\frac{1}{m_i}=\sum\frac{1}{n_j}\implies\sum m_i\neq\sum n_j?$

Published on 30 Jan 2024 - 8:43

score 141 · Answer 15 · 2024-03-07 12:23:05

141

Views

A game of magic Egyptian tilings

Published on 07 Mar 2024 - 12:23

List Question

how to find number of presentation of 1 as a sum of $2^{-i}$?

The longest sequence of unique unit fractions that sums to 1, given a specific bound on the denominators

$A = \sum_{i=1}^{\infty} \frac{i}{a_i}$ and $1 = \sum_{i=1}^{\infty} \frac{1}{a_i}$?

Reference Request - Online copy of R. Graham's "On Finite Sums of Rational Numbers"

Is there a finite set of distinct naturals whose reciprocals sum to 1, and no element in the set is one less than a prime?

What is known about the average growth rate of the denominators of $n$ Egyptian fractions summing to one?

Four different positive integers whose reciprocals sum to 1

Expressing one as a sum of unique unit fractions whose denominators are increasing?

Have the prime Egyptian fractionary expansions of rational numbers been studied before?

Egyptian fraction of length 3 in the interval (0.5,1)

Egyptian fraction of a number in the interval (0.5,1)

Has the diophantine equation $ \sum_{n=1}^{N} \frac{1}{x_{n}} = \prod_{k=1}^{N} \left(1-\frac{1}{x_{k}} \right) $ been studied?

Conjecture: If $\sum_{i=1}^n \frac{1}{x_i}=1$ then $x_i | x_j$

$m_i, n_j$ integers and $\{m_i\}_{i=1}^{k}\neq\{n_j\}_{j=1}^{k'}.$ Does $\sum\frac{1}{m_i}=\sum\frac{1}{n_j}\implies\sum m_i\neq\sum n_j?$

A game of magic Egyptian tilings

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