Smarandache Notions Journal, Vol. 10

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Vol. 10, No. 1-2-3, Spring 1999 ISSN 1084-2810

SMARANDACHE NOTIONS JOURNAL

Number Theory Associationof the

UNIVERSITY OF CRAIOVA


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ASSOCIATE EDITORIAL BOARD:

Charles Ashbacher, Charles Ashbacher Technologies, Box 294,119 Northwood Drive, Hiawatha, Iowa 52233, USA.

Mihaly Bencze, Str. H|rmanului 6, 2212 S|cele 3, Jud. Braov,Romania.

Emil Burton, Department of Mathematics, University of Cluj-Napoca, Romania.

Ion Cojocaru & Sorin Cojocaru, Department of Mathematics,University of Craiova, Romania.

Constantin Corduneanu, Department of Mathematics, Universityof Texas at Arlington, USA.

Henry Ibstedt, Glimminge 2036, 280 60 Broby, Sweden.Widmer Lamarr, Department of Mathematics, Mesiah College,

Grantham, PA 17027, USA. Maohua Le, Department of Mathematics, Zhanjiang Normal

College, 29 Cunjin Road, Chikan, Zhanjiang, Guangdong, P.R.China.

A.A.K. Majumdar, Department of Mathematics, JahangirnagarUniversity, Savar, Dhaka 1342, Bangladesh.

Mike Mudge, 22 Gors Fach, Pwll-Trap, St Clears,Carmarthenshire, Dyfed SA33 4AQ, United Kingdom.

Jean Normand, 3, square Robinson, 92330 Sceaux, France.Stefan Porubsky, Department of Mathematics, Institute of

Chemical Technology, Technicka 1905, 16628 Prague 6, CzechRepublic.

E. R|descu & N. R|descu, Department of Mathematics,University of Craiova, Romania.

Carmen Rocoreanu, Department of Mathematics, University ofCraiova, Romania.

Francisco Bellot Rosado, Dos de Mayo 16-8E dcha, E-47004Valladolid, Spain.

Jozsef Sandor, Department of Mathematics, Babe-BolyaiUniversity, 3400 Cluj-Napoca, Romania.

Y. A. Shmagin, Department of Mathematics, St.-PetersburgTechnical University, Nevsky 3-11, 191186,St.-Petersburg, Russia.

Vera W. de Spinadel, Centro de Matematica y Diseno MAyDI,Facultad de Arquitectura, Diseno y Urbanismo, Universidadde Buenos Aires, Argentina.

Homer B. Tilton, Department of Mathematics, Phisics, andAstronomy, Pima Community College, Tucson, Arizona, USA.


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INDICATION TO AUTHORS

Authors of papers concerning any of Smarandache type functions,

numbers, sequences, integer algorithms, paradoxes, experimentalgeometries, etc. are encouraged to submit manuscripts to theEditors:

V. Seleacu & I. B|l|cenoiuDepartment of MathematicsUniversity of Craiova, Romania.

The submitted manuscripts may be in the format of remarks,conjectures, solved/unsolved or open new proposed problems, notes,articles, miscellaneous, etc. They must be original work and

camera ready [typewritten/computerized, format: 8.5 x 11 inches (.21,6 x 28 cm)]. They are not returned, hence we advise theauthors to keep a copy.The title of the paper should be writting with capital letters.The author's name has to apply in the middle of the line, nearthe title. References should be mentioned in the text by a numberin square brackets and should be listed alphabetically. Currentaddress followed by e-mail address should apply at the end of thepaper, after the references.

The paper should have at the beginning an up to a half-pageabstract, followed by the key words.All manuscripts are subject to anonymous review by two or moreindependent sources.Every letter will be answered.

The authors will receive free copies of the journal.

Papers in electronic form are accepted. They can be e-mailed inMicrosoft Word 7.0a (or lower) for Windows 95, WordPerfect 6.0 (orlower) for Windows 95, or text files.


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C O N T E N T S

ARTICLES:Micha Fleuren, Smarandache Factors and Reverse Factors ..... 5

Henry Ibstedt, Smarandache Continued Fractions ............. 39Constantin Dumitrescu, Carmen Rocsoreanu, Some ConnectionsBetween the Smarandache Function and the Fibonnaci Sequence . 50Y. V. Chebrakov, V. V. Shmagin, Computative Paradoxes inModern Data Analysis ........................................ 61Kevin Ford, The Normal Behavior of the Smarandache Function 81J. Sndor, On Values of Arithmetical Functions atFactorials I ................................................ 87Steven R. Finch, The Average Value of the SmarandacheFunction .................................................... 95Sabin Tabirca, Smarandache Magic Squares ................... 100

Sabin Tabirc|, Tatiana Tabirc|, Some Inequalities ConcerningSmarandache's Function ...................................... 105

Sebastin Martn Ruiz, Smarandache's Function Applied toPerfect Numbers ............................................. 114Florian Luca, On the Divergence of the Smarandache HarmonicSeries ...................................................... 116

Sabin Tabirc|, Tatiana Tabirc|, A Generalization of Euler'sFunction .................................................... 119Sebastin Martn Ruiz, A Result Obtained Using Smarandache'sFunction .................................................... 123

J. Sndor, On An Inequality for the Smarandache Function...125

Florian Luca, On A Series Involving S(1)@S(2)...@S(n) ..... 128Sebastin Martn Ruiz, A Congruence with Smarandache'sFunction .................................................... 130

Henry Ibstedt, An Integer as a Sum of Consecutive Integers . 133

NOTES:Mihaly Bencze, A New Inequality for the Smarandache Function 139Maohua Le, A Formula for the Smarandache Function .......... 140Maohua Le, On the Diophantine Equation S(n) = n ............ 142Maohua Le, On Smarandache Divisor Product .................. 144Maohua Le, On the Smarandache n-ary Sieve .................. 146Maohua Le, Perfect Powers in the Smarandache PermutationSequence .................................................... 148Maohua Le, On Smarandache Pseudo-Powwers of Third Kind ..... 150

Maohua Le, An Improvement on the Smarandache DivisibilityTheorem ..................................................... 152Maohua Le, On Primes in the Smarandache Pierced Chain ...... 154

4 4Maohua Le, Primes in the Sequences {nn+1}n=1 and {n

n+1}n=1 . 156

Maohua Le, On the Smarandache Prime Additive ComplementSequence .................................................... 158


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Mihaly Bencze, An Inequality for the Smarandache Function .. 160Maohua Le, On Smarandache Simple Functions ................. 161Charles Ashbacher, Maohua Le, On Smarandache Simple ContinuedFractions ................................................... 163Maohua Le, Notes on Primes Smarandache Progressions ........ 165Maohua Le, The Primes p with lg(p) = 1 ..................... 167

Maohua Le, Some Solutions of the Smarandache Prime Equation 169Charles Ashbacher, Smarandache Series Converges ............. 171

4Maohua Le, A Note on Primes in the Sequence {an+b}n=1 ...... 172Maohua Le, The Primes in the Smarandache Symmetric Sequence 174Maohua Le, On Smarandache General Continued Fractions ...... 176

Maohua Le, The Lower Bound for the Smarandache CounterC(0,n!) ..................................................... 178

Maohua Le, On Smarandache Pseudo-Primes of Second Kind .... 180

MATHEMATICAL HISTORY:Henry Ibstedt, Summary of the First International Conferenceon Smarandache Type Notions in Number Theory (University ofCraiova, August 21-24, 1997) ................................ 181Henry Ibstedt, Preambul to the First International Conferenceon Smarandache Type Notions in Number Theory (University ofCraiova, August 21-24, 1997) ................................ 182Henry Ibstedt, The Smarandache Sequence Inventory .......... 183Henry Ibstedt, List of Smarandache Documents ............... 191

I. B|l|cenoiu, V. Seleacu, History of the SmarandacheFunction .................................................... 192J. Castillo, Other Smarandache Type Functions .............. 202

M. L. Perez, Survey on the Research of Smarandache Notions 205

REVIEWS:Book Reviews ................................................ 207


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Smarandache Notions Journal, Vol. 10

Documents

Transcript of Smarandache Notions Journal, Vol. 10