# Tagged Questions

An arithmetic progression is a (possibly infinite) sequence of numbers such that the difference between consecutive terms is always the same value.

575 views

### What are the limits of the Erdős-Rankin method for covering intervals by arithmetic progressions?

To construct gaps between primes which are marginally larger than average, Erdős and Rankin covered an interval $[1,y]$ with arithmetic progressions with prime differences. A nice short exposition is ...
337 views

315 views

Let $A=(a_n : n \in \mathbb{N})$ be the sequence given by: $$\ a_n = a_1 + (n - 1)d,\quad a_1,\ d,\ n \in \mathbb N,\quad d\gt a_1,\quad \gcd(a_1,\ d)=1.$$ For all terms of $A$ greater than $\ \... 0answers 116 views ### Arithmetic progression and 3^m,3^{m+1} intervals I'm trying to prove (or disprove) the following "conjecture".Given the following set of powers of two: $$A = \{ x \mid x = 2^n \text{ and } 2^{n-1} < 3^m < x < 3^{m+1} < 2^{n+1}\}$$ (... 0answers 211 views ### Conjecture about distribution of primes in arithmetic progression For my work, i need the following Conjecture: Let$N$large number such that exist a prime number$q$and$A>\frac{1}{2}$such that$N^{1/2}<N^{A}\leq q-1<N.$Then$\forall a\in\left[1,\, q\...
If $S_k$ is the greedy sequence with no length-k arithmetic subsequence, (ie $S_3$ = A003278 , $S_4$ = A005837 , $S_5$ = A020655 ), is it guaranteed that any other sequence $a$ with no length-k ...
"I took number $3$ and observed: $3$ is an arithmetic progression of length one. $3,5$ is an arithmetic progression of length two. $3,5,7$ is an arithmetic progression of length three. Then I took ...