Runs of integers with equally many distinct prime factors

Title: Runs of integers with equally many distinct prime factors
Creator: Eggleton, Roger B.; Kimberley, Jason S.; MacDougall, James A.
Relation: Bulletin of the Institute of Combinatorics and its Applications Vol. 64, p. 30-38
Relation: http://www.theica.org
Publisher: Institute of Combinatorics and its Applications
Resource Type: journal article
Date: 2012
Description: We survey and update data on runs of consecutive integers each having exactly r distinct prime factors (briefly, of principal rank r). For 3 ≤ r ≤ 64 and other sporadic values, lower bounds are given for the size of longest runs of consecutive integers of principal rank r, together with upper bounds on the first occurrence of such runs. We also prove that there are infinitely many pairs of consecutive integers of principal rank r, for each r ≥ 3.
Subject: 11A51; factorisation; consecutive integers; sieve methods; Chinese Remainder Theorem
Identifier: http://hdl.handle.net/1959.13/933758
Identifier: uon:11712
Identifier: ISSN:1183-1278
Language: eng
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