Sequences Research Papers - Academia.edu (original) (raw)

About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. Because this is too vast to be covered in one book, we divide encyclopedia in more volumes. We are going to structure this volume of encyclopedia in six parts: the first will cover the Smarandache type sequences and series (obviously, among them there are the well-known sequences of numbers obtained through concatenation but also numerous other sequences), the second part will cover the Smarandache type functions and constants, the third part will cover the conjectures on Smarandache notions and the conjectures on number theory due to Florentin Smarandache, the fourth part will cover the theorems on Smarandache notions and the theorems on number theory due to Florentin Smarandache, the fifth part will cover the criteria, formulas and algorithms for computing due to Florentin Smarandache and the sixth part will cover the unsolved problems regarding Smarandache notions and the open problems on number theory due to Florentin Smarandache. Obviously, the division into these chapters has mostly the role to organise the matters treated, not to delineate them one from another, because all are related; for instance, a function treated in chapter about functions may create a sequence treated in chapter about sequences or a conjecture about primes treated in the chapter about primes may involve a diophantine equation, though these ones have their own chapter. Similarly, we presented some conjectures, theorems and problems on sequences or functions in the chapters dedicated to definition of the latter, while we presented other conjectures, theorems and problems on the same sequences or functions in separate chapters; we could say we had a certain vision doing so (for instance that we wanted to keep a proportion between the sizes of the sections treating different sequences or functions and not to interrupt the definitions between two related sequences or functions by a too large suite of problems) but it would not be entirely true: the truth is that a work, once started, gets its own life and one could say that almost it dictates you to obey its internal order.