Sequences and series involving the sequence of composite numbers
oleh: Panayiotis Vlamos
| Format: | Article |
|---|---|
| Diterbitkan: | Wiley 2002-01-01 |
Deskripsi
Denoting by pn and cn the nth prime number and the nth composite number, respectively, we prove that both the sequence (xn)n≥1, defined by xn=∑k=1n (ck+1−ck) / k−pn / n, and the series ∑n=1∞ (pcn−cpn) / npn are convergent.