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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
ON CONVOLUTION OF SOME TYPE OF THE NUMBERS CONNECTED WITH GENERALIZED REPUNITS
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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