SEQUENCES OF INTEGERS, CONJECTURES AND NEW ARITHMETICAL TOOLS (COLLECTED PAPERS)

Book excerpt: Part One of this book of collected papers brings together papers regarding conjectures on primes, twin primes, squares of primes, semiprimes, different types of pairs of primes, recurrent sequences, other sequences of integers related to primes created through concatenation and in other ways. Part Two brings together several articles presenting the notions of c-primes, m-primes, c-composites and m-composites (c/m integers), also the notions of g-primes, s-primes, g-composites and s-composites (g/s integers) and show some of the applications of these notions. Part Three presents the notions of “Mar constants” and “Smarandache-Coman constants”, useful to highlight the periodicity of some infinite sequences of positive integers (sequences of squares, cubes, triangualar numbers) , respectively in the analysis of Smarandache concatenated sequences. Part Four presents the notion of Smarandache-Coman sequences, id est the sequences of primes formed through different arithmetical operations on the terms of Smarandache concatenated sequences. Part Five presents the notion of Smarandache-Coman function, a function based on the Smarandache function which seems to be particularly interesting: beside other notable characteristics, it seems to have as values all the prime numbers and, more than that, they seem to appear, leaving aside the non-prime values, in natural order. This book of collected papers seeks to expand the knowledge on some well known classes of numbers and also to define new classes of primes or classes of integers directly related to primes.