Felice Russo's A set of new Smarandache functions, sequences and PDF

By Felice Russo

ISBN-10: 1879585839

ISBN-13: 9781879585836

Show description

Read Online or Download A set of new Smarandache functions, sequences and conjectures in number theory PDF

Similar theory books

Read e-book online Advances in the Theory of Quantum Systems in Chemistry and PDF

Advances within the concept of Quantum structures in Chemistry and Physics is a suite of 32 chosen papers from the medical contributions awarded on the fifteenth foreign Workshop on Quantum platforms in Chemistry and Physics (QSCP-XV), held at Magdalene collage, Cambridge, united kingdom, from August thirty first to September fifth, 2010.

Download e-book for iPad: Bounded Queries in Recursion Theory by William I. Gasarch, Georgia A. Martin (auth.)

One of many significant matters of theoretical desktop technology is the classifi­ cation of difficulties by way of how not easy they're. The average degree of trouble of a functionality is the volume of time had to compute it (as a functionality of the size of the input). different assets, reminiscent of area, have additionally been thought of.

Download e-book for kindle: Understanding Children's Behaviour 0-11 Years by Jennie Lindon

This ebook gives you a mix of sensible rules and underpinning idea approximately how young ones research styles of behaving. This e-book will help you think of reasonable expectancies for various age teams, the most likely views of youngsters, and may consultant you to house teenagers whose habit is skilled as difficult.

Additional resources for A set of new Smarandache functions, sequences and conjectures in number theory

Example text

6. The function has been applied to the power sequence [2]. 97 91 85 79 73 67 61 55 49 43 37 31 25 19 13 7 180 160 140 120 100 80 60 40 20 0 1 Ss(n) Smarandache Summatory Divisor Function for Smarandache power sequence n Fig. 3275 K Problem 25. Is there any Smarandache sequence a(n) such that the following inequality is satisfied? 2 ⋅ (1 − 2 ) + g − ln(4 ⋅ π ) Ss(n ) ≤ eg + a( n) ⋅ ln(ln( a( n))) ln(a (n)) ⋅ ln(ln( a(n ))) where g is the Smarandache Euler-Mascheroni constant for the sequence a(n).

20 The diophantine equation Zw(n)=Zw(n+1) has no solutions. Proof. In fact according to the previous theorem if n is even (odd respectively) then Zw(n) also is even (odd respectively). Therefore the equation Zw(n)=Zw(n+1) can not be satisfied because Zw(n) that is even should be equal to Zw(n+1) that instead is odd. 21 Zw( n + 1) The equations =k Zw(n )  Zw (n + 1)   and   Zw( n)  −1 =k with k any positive integer and n>1 for the first equation don't admit solutions. Proof. We must consider three cases: 1.

513624.... 031646....... 239704.... 75843....... If F is close to an integer we call it a Smarandache almost integer. Problem 19. Is there any Smarandache sequence a(n) that produce other Smarandache almost integers? 4 The Smarandache Dirichlet Eta function for the Smarandache power sequence [2] diverge for s<3. 22) Smarandache Dirichlet Lambda Function Let a(n) be any Smarandache sequence. 5 The Smarandache Dirichlet lambda function for the power sequence [2] diverge for s<5. Problem 20. Is there any Smarandache sequence a(n) such that: Sz ( s) + Se( s) = 2 ⋅ Sl (s ) for some s ∈ N , where Sz(s) is the Smarandache Zeta function and Se(s) the Smarandache Dirichlet Eta function?

Download PDF sample

A set of new Smarandache functions, sequences and conjectures in number theory by Felice Russo

by Thomas

Rated 4.59 of 5 – based on 43 votes