On a result of Flammenkamp-Luca concerning noncototient sequence
type: Item
instance of: scholarly article
title: On a result of Flammenkamp-Luca concerning noncototient sequence
zbMATH Open document ID: 1090.11003
author: Aleksander Grytczuk
author: Barbara Mȩdryk
published in: Tsukuba Journal of Mathematics
publication date: 2006-04-06T00:00:00Z
review text: The author finds some interesting properties of the Sierpiński sequence. He proves the following theorems: (I) Let \(p\) be an odd prime. The sequence \((2^{k}p), k=1,2, \dots\) is the Sierpiński sequence if and only if: 1) \(2p\) is a noncototient, 2) \(p\) is not a Mersenne prime, 3) \(2^{k}p-1\) is composite for every positive integer \(k \geq1\). (II) There are infinitely many primes \(p\) in the arithmetical progression \( m\prod q_{j}+p_{0}\), where \(p_{0} = 509203\), \(\prod q_{j} = 3\times 5 \times 7 \times 13 \times 17 \times 241 \) such that: 1) \(2^{k}p-1\) is composite for every positive integer \( k\geq1\), 2) \(p\) is not a Mersenne prime. (III) The number \(2p\), where \(p\) is an odd prime of the form \(n-\varphi (n)\) if and only if there are different odd primes \( p_{j}\), where \(j = 1,2,\dots,r\), \(r\geq1\) such that \(p = p_{1}p_{2}\dots p_{r}-\frac{1}{2}(p_{1}-1)(p_{2}-1)\dots(p_{r}-1)\).
reviewed by: Jebrel M. Habeb
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11A05
zbMATH DE Number: 5017538
zbMATH Keywords: Flammenkamp-Luca result
zbMATH Keywords: Noncototient sequence
zbMATH Keywords: Euler totient function
zbMATH Keywords: Sierpiński sequence.
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496164969
OpenAlex ID: W390714252
DOI: 10.21099/TKBJM/1496164969
description: scientific article; zbMATH DE number 5017538