ON CONVOLUTION OF SOME TYPE OF THE NUMBERS CONNECTED WITH GENERALIZED REPUNITS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F13%3A50001457" target="_blank" >RIV/62690094:18470/13:50001457 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.ijpam.eu/contents/2013-82-4/10/10.pdf" target="_blank" >http://www.ijpam.eu/contents/2013-82-4/10/10.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.12732/ijpam.v82i4.10" target="_blank" >10.12732/ijpam.v82i4.10</a>

Jazyk výsledku

angličtina

Název v původním jazyce

ON CONVOLUTION OF SOME TYPE OF THE NUMBERS CONNECTED WITH GENERALIZED REPUNITS

Popis výsledku v původním jazyce

The term repunit was coined by Beiler in 1966. A repunit Rn is any integer written in decimal form as a string of 1?s. The numbers 1, 11, 111, 1111, 11111, etc., are examples of repunits. Thus repunits have the form Rn = (10^n-1)/9 . The great effort wasdevoted to searching of repunit primes, thus such primes which are any repunits and they are also prime numbers. Snyder extended the notation repunit to one in which for some integer b >= 2 by this way Rn(b) = (b^n-1)/ (b-1). They are called as generalized repunits or repunits to base b and consist of a string of 1?s when written in base b. In this paper we will investigate a generalization of generalized repunits Rn(k+1), which are created by subtracting the linear term in (k+1)^n and dividing by thetrivial divisor k^2, thus Jn(k) = ((k + 1)^n - nk - 1)/k^2. In this paper some results about divisibility of Jn(k) are stated. Further the generating function and a m-fold convolution formula for the numbers Jn(k) is found.

Název v anglickém jazyce

ON CONVOLUTION OF SOME TYPE OF THE NUMBERS CONNECTED WITH GENERALIZED REPUNITS

Popis výsledku anglicky

The term repunit was coined by Beiler in 1966. A repunit Rn is any integer written in decimal form as a string of 1?s. The numbers 1, 11, 111, 1111, 11111, etc., are examples of repunits. Thus repunits have the form Rn = (10^n-1)/9 . The great effort wasdevoted to searching of repunit primes, thus such primes which are any repunits and they are also prime numbers. Snyder extended the notation repunit to one in which for some integer b >= 2 by this way Rn(b) = (b^n-1)/ (b-1). They are called as generalized repunits or repunits to base b and consist of a string of 1?s when written in base b. In this paper we will investigate a generalization of generalized repunits Rn(k+1), which are created by subtracting the linear term in (k+1)^n and dividing by thetrivial divisor k^2, thus Jn(k) = ((k + 1)^n - nk - 1)/k^2. In this paper some results about divisibility of Jn(k) are stated. Further the generating function and a m-fold convolution formula for the numbers Jn(k) is found.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International journal of pure and applied mathematics

ISSN

1311-8080

e-ISSN

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Svazek periodika

82

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

BG - Bulharská republika

Počet stran výsledku

7

Strana od-do

615-621

Kód UT WoS článku

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EID výsledku v databázi Scopus

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