For J 3 (n) = p 1 +p 2 +p 3 =n p 1 โกa 1 (mod q 1 ) log p 1 log p 2 log p 3 , it is shown that for any A and any < 1/2, what improves a work of Tolev; S 3 (n) is the corresponding singular series. A special form of a sieve of Montgomery is used.
On the upper bound for the number of primes or almost primes in a given integer sequence
โ Scribed by J. Kan
- Publisher
- Springer Netherlands
- Year
- 1991
- Tongue
- English
- Weight
- 327 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0031-5303
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๐ SIMILAR VOLUMES
Let G be a connected and simple graph, and let i(G) denote the number of stable sets in G. In this letter, we have presented a sharp upper bound for the i(G)-value among the set of graphs with k cut edges for all possible values of k, and characterized the corresponding extremal graphs as well.
We show that an n-vertex bipartite K 3,3 -free graph with n 3 has at most 2n -4 edges and that an n-vertex bipartite K 5 -free graph with n 5 has at most 3n -9 edges. These bounds are also tight. We then use the bound on the number of edges in a K 3,3 -free graph to extend two known NC algorithms fo