# On sums of a Sidon-sequence

```@article{Erdos1991OnSO,
title={On sums of a Sidon-sequence},
author={Paul L. Erdos and R{\'o}bert Freud},
journal={Journal of Number Theory},
year={1991},
volume={38},
pages={196-205}
}```
• Published 1 June 1991
• Mathematics
• Journal of Number Theory
19 Citations
Gaps in dense sidon sets
We prove that if A ⊂ [1, N ] is a Sidon set with N1/2−L elements, then any interval I ⊂ [1, N ] of length cN contains c|A|+EI elements of A, with |EI | ≤ 52N(1+ c1/2N1/8)(1+L + N−1/8), L+ = max{0,
On Sum Sets of Sidon Sets, 1.
• Mathematics
• 1994
It is proved that there is no Sidon set selected from {1, 2, …,N} whose sum set containsc1N1/2 consecutive integers, but it may containc2N1/3 consecutive integers. Moreover, it is shown that a finite
On sum sets of sidon sets, II
• Mathematics
• 1995
It is proved that there is no Sidon set selected from {1, 2, …,N} whose sum set containsc1N1/2 consecutive integers, but it may containc2N1/3 consecutive integers. Moreover, it is shown that a finite
Random Sidon Sequences
• Mathematics
• 1999
A subset A of the set [n] = {1, 2,..., n}, \A\ = k, is said to form a Sidon (or B-h) sequence, h greater than or equal to 2, if each of the sums a(1) + a(2) +...+ a(h), a(1) less than or equal to
SIDON SETS WITH SMALL GAPS
• Mathematics
• 1995
Let N denote the set of positive integers. A set A⊂N is called a Sidon set if the sums a + a (a, a∊A) are all distinct. For background on Sidon sets, we refer to [6]. For additional recent results
B h sequences
Let A be a set (finite or infinite) of natural numbers, and let a i denote a generic element of A. We say that A is a B h sequence if the sums of the form a 1 + … + a h (a 1 ≤ … ≤ a h ) are all
Well Distribution of Sidon Sets in Residue Classes
Abstract A set A of non-negative integers is a Sidon set if the sums a + b ( a ,  b ∈ A ,  a ⩽ b ) are distinct. Assume that a ⊆[1,  n ] and that | A |=(1+ o (1)) n 1/2 . Let m ⩾2 be an integer. In
INTEGER SETS HAVING THE MAXIMUM NUMBER OF DISTINCT DIFFERENCES
• Mathematics
• 2007
In this paper we study the function D(k,n) which is the maximum of |A ! A| = ! {a ! b : a,b " A} ! over all k-subsets A of {0,...,n}. We prove that for any fixed real c # 0 and any function k(n) = (c
Extremal Sidon sets are Fourier uniform, with applications to partition regularity
• Mathematics
• 2021
Generalising results of Erdős-Freud and Lindström, we prove that the largest Sidon subset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. We establish this by showing
Continuous Ramsey Theory and Sidon Sets
• Mathematics
• 2002
A symmetric subset of the reals is one that remains invariant under some reflection x --> c-x. Given 0 D(x), then there exists a subset of [0,1] with measure x that does not contain a symmetric

## References

On a problem of sidon in additive number theory, and on some related problems
• Mathematics
• 1941
To the memory of S. Sidon. Let 0 < a, < a,. .. be an infinite sequence of positive integers. Denote by f(n) the number of solutions of n=a i +a;. About twenty years ago, SIDON 1) raised the question