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

2015-01-01 Mathematics

Author : Marius Coman
Release : 2015-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 439/5 ( reviews)

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Book Synopsis SEQUENCES OF INTEGERS, CONJECTURES AND NEW ARITHMETICAL TOOLS (COLLECTED PAPERS) by : Marius Coman

Download or read book SEQUENCES OF INTEGERS, CONJECTURES AND NEW ARITHMETICAL TOOLS (COLLECTED PAPERS) written by Marius Coman. This book was released on 2015-01-01. Available in PDF, EPUB and Kindle. 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.

Sequences of Primes Obtained by the Method of Concatenation (Collected Papers)

2016 Mathematics

Author : Marius Coman
Release : 2016
Genre : Mathematics
Kind : eBook
Book Rating : 664/5 ( reviews)

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Book Synopsis Sequences of Primes Obtained by the Method of Concatenation (Collected Papers) by : Marius Coman

Download or read book Sequences of Primes Obtained by the Method of Concatenation (Collected Papers) written by Marius Coman. This book was released on 2016. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to show that the method of concatenation can be a powerful tool in number theory and, in particular, in obtaining possible infinite sequences of primes. Part One of this book, “Primes in Smarandache concatenated sequences and Smarandache-Coman sequences of primes” , contains 12 papers on various sequences of primes that are distinguished among the terms of the well known Smarandache concatenated sequences. The sequences presented in this part are related to concatenation in three different ways: the sequence is obtained by the method of concatenation but the operation applied on its terms is some other arithmetical operation; the sequence is not obtained by concatenation but the operation applied on its terms is concatenation or both the sequence and the operation applied on its terms (in order to find sequences of primes) are using the method of concatenation. Part Two of this book, “Sequences of primes obtained by the method of concatenation” brings together 51 articles which aim, using the mentioned method, to highlight sequences of numbers which are rich in primes or are liable to lead to large primes. The method of concatenation is applied to different classes of numbers, e.g. Poulet numbers, twin primes, reversible primes, triangular numbers, repdigits, factorial numbers, fibonorial numbers, primordial numbers in order to obtain sequences of primes.

Sequences of Numbers Involved in Unsolved Problems

2006-01-01 Mathematics

Author : Florentin Smarandache
Release : 2006-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 065/5 ( reviews)

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Book Synopsis Sequences of Numbers Involved in Unsolved Problems by : Florentin Smarandache

Download or read book Sequences of Numbers Involved in Unsolved Problems written by Florentin Smarandache. This book was released on 2006-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. The book contains definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. ( on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes/squares/cubes/factorials, almost primes, mobile periodicals, functions, tables, prime/square/factorial bases, generalized factorials, generalized palindromes, etc. ).

Mathematics and Computation

2019-10-29 Computers

Author : Avi Wigderson
Release : 2019-10-29
Genre : Computers
Kind : eBook
Book Rating : 137/5 ( reviews)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson. This book was released on 2019-10-29. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Mathematical Reviews

2003 Mathematics

Author :
Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Download or read book Mathematical Reviews written by . This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt:

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

Sequences of Primes Obtained by the Method of Concatenation (Collected Papers)

Sequences of Numbers Involved in Unsolved Problems

Mathematics and Computation

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