Abstract
Let A be a sequence of natural numbers, r A(n) be the number of ways to represent n as a sum of consecutive elements in A, and M A(x) := ∑ n ≤ x r A(n). We give a new short proof of LeVeque's formula regarding M A(x) when A is an arithmetic progression, and then extend the proof to give asymptotic formulas for the case when A behaves almost like an arithmetic progression, and also when A is the set of primes in an arithmetic progression.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1281-1299 |
| Number of pages | 19 |
| Journal | International Journal of Number Theory |
| Volume | 8 |
| Issue number | 5 |
| DOIs | |
| State | Published - Aug 2012 |
Keywords
- Consecutive integer
- arithmetic progression
- prime number
- representation
ASJC Scopus subject areas
- Algebra and Number Theory