DOI•
On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers
09 Apr 2019-
About: The article was published on 2019-04-09 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Mersenne prime.
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TL;DR: The generalized entropies of C. Tsallis and G. Kaniadakis have composition operations, which can be applied to the study of numbers and are used to study some famous sequences of numbers.
Abstract: The generalized entropies of C. Tsallis and G. Kaniadakis have composition operations, which can be applied to the study of numbers. Here we will discuss these composition rules and use them to study some famous sequences of numbers (Mersenne, Fermat, Cullen, Woodall and Thabit numbers). We will also consider the sequence of the repunits, which can be seen as a specific case of q-integers.
6 citations
TL;DR: In this paper, the groupoids related to the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers have been studied using the On-Line Encyclopedia of Integer Sequences (OEIS).
Abstract: In some previous works, we have discussed the groupoids related to the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers. These groupoids possess different binary operators. As we can easily see, other integer sequences can have the same binary operators, and therefore can be used to represent the related groupoids. Using the On-Line Encyclopedia of Integer Sequences (OEIS), we are able to identify the properties of these representations of groupoids. At the same time, we can also find integer sequences not given in OEIS and probably not yet studied.
4 citations
References
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TL;DR: The generalized entropies of C. Tsallis and G. Kaniadakis have composition operations, which can be applied to the study of numbers and are used to study some famous sequences of numbers.
Abstract: The generalized entropies of C. Tsallis and G. Kaniadakis have composition operations, which can be applied to the study of numbers. Here we will discuss these composition rules and use them to study some famous sequences of numbers (Mersenne, Fermat, Cullen, Woodall and Thabit numbers). We will also consider the sequence of the repunits, which can be seen as a specific case of q-integers.
6 citations
TL;DR: In this paper, the groupoids related to the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers have been studied using the On-Line Encyclopedia of Integer Sequences (OEIS).
Abstract: In some previous works, we have discussed the groupoids related to the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers. These groupoids possess different binary operators. As we can easily see, other integer sequences can have the same binary operators, and therefore can be used to represent the related groupoids. Using the On-Line Encyclopedia of Integer Sequences (OEIS), we are able to identify the properties of these representations of groupoids. At the same time, we can also find integer sequences not given in OEIS and probably not yet studied.
4 citations