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Smarandache Sequences, Stereograms and Series

By Charles Ashbacher

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Book Id: WPLBN0002097036
Format Type: Default
File Size: 435 KB
Reproduction Date: 8/30/2011

Title: Smarandache Sequences, Stereograms and Series  
Author: Charles Ashbacher
Volume:
Language: English
Subject: Non Fiction, Education, Mathematics
Collections: Mathematics, Algebra, Authors Community, Arithmetic, Special Collection Mathematics, Math, Education, Medicine, Literature, Law
Historic
Publication Date:
Publisher: Hexis and Charles Ashbacher
Member Page: PG Reading Room

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Ashbacher, C. (n.d.). Smarandache Sequences, Stereograms and Series. Retrieved from http://www.gutenberg.cc/


Description
F. Smarandache has defined many sequences of integers formed by concatenating the positive integers in specific ways. A question that is often asked about most of these sequences concerns the number of primes in the sequence. As Paul Erdos pointed out, determining how many primes are in sequences of this type is a problem that the current state of mathematical knowledge is unprepared to solve. In general, the sequences grow rather fast, so after a very short time, the terms are too large for modern computers to determine if they are prime. The only hope is to find some property of the elements of the sequence that can be used to very quickly determine if it can be factored.

Excerpt
Using the bases from three through nine to form new sequences, we can then ask the same question regarding the number of primes in the sequence. That appears to be a question just as difficult as the one for base ten numbers, and is summarized in the following statement.

Table of Contents
Preface.3 -- Table of Contents.4 -- Chapter 1 Sequences Formed by Concatenating All the Positive Integers.5 -- Chapter 2 Sequences Formed by Concatenating Selected Natural Numbers .44 -- Chapter 3 Smarandache Stereograms .70 3.1 -- The Stereogram.70 -- 3.2 Altering the Background.87 -- 3.3 Additional Stereograms .91 -- 3.4 Possibilities for Additional Figures .92 -- Chapter 4 Constants Involving the Smarandache Function .95 -- Index.133 --

 

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