We briefly describe some well known means and their properties, focusing on the relationship with integer sequences. In particular, the harmonic numbers, deriving from the harmonic mean, motivate the definition of a new kind of mean that we call the biharmonic mean. The biharmonic mean allows to introduce the biharmonic numbers, providing a new characterization for primes. Moreover, we highlight some interesting divisibility properties and we characterize the semi prime biharmonic numbers showing their relationship with linear recurrent sequences that solve certain Diophantine equations.
The biharmonic mean / Abrate, Marco; Barbero, Stefano; Cerruti, Umberto; Murru, Nadir. - In: MATHEMATICAL REPORTS. - ISSN 1582-3067. - 18:4(2016), pp. 483-495.
The biharmonic mean
Barbero, Stefano;Murru, Nadir
2016-01-01
Abstract
We briefly describe some well known means and their properties, focusing on the relationship with integer sequences. In particular, the harmonic numbers, deriving from the harmonic mean, motivate the definition of a new kind of mean that we call the biharmonic mean. The biharmonic mean allows to introduce the biharmonic numbers, providing a new characterization for primes. Moreover, we highlight some interesting divisibility properties and we characterize the semi prime biharmonic numbers showing their relationship with linear recurrent sequences that solve certain Diophantine equations.| File | Dimensione | Formato | |
|---|---|---|---|
|
biharmonic3.pdf
accesso aperto
Tipologia:
Post-print referato (Refereed author’s manuscript)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
264.53 kB
Formato
Adobe PDF
|
264.53 kB | Adobe PDF | Visualizza/Apri |
|
biharmonic.pdf
Solo gestori archivio
Tipologia:
Versione editoriale (Publisher’s layout)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
261.26 kB
Formato
Adobe PDF
|
261.26 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
