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.
Highlights
IntroductionThe only restriction on the operator is closure
A groupoid is an algebraic structure made by a set with a binary operator [1]
We can find integer sequences not given in OEIS and probably not yet studied
Summary
The only restriction on the operator is closure This property means that, applying the binary operator to two elements of a given set S, we obtain a value which is itself a member of S. As shown in some previous works [2,3,4,5,6,7], the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers are groupoid possessing different binary operators. We can obtain different integer sequences by means of the recurrence relations generated by the considered binary operations. In [7], we started the search for different representations for the groupoid of Triangular Numbers We generalize this search, using the binary operators obtained in the previous analyses. We can find integer sequences not given in OEIS and probably not yet studied
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