By Felice Russo

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

**Similar theory books**

**Coverings of Discrete Quasiperiodic Sets (Springer Tracts in Modern Physics)**

During this up to date assessment and advisor to latest literature, the professional authors boost thoughts concerning quasiperiodic coverings and describe effects. The textual content describes particular platforms in 2 and three dimensions with many illustrations, and analyzes the atomic positions in quasicrystals.

**Evolutionary Instability: Logical and Material Aspects of a Unified Theory of Biosocial Evolution**

The new sociobiology debate has raised primary and formerly unresolved conceptual difficulties. Evolutionary Instability - Logical and fabric elements of a Unified concept of Biosocial Evolution - bargains ap- proaches for his or her resolution. The clinical functions include the dynamics and evolutionary instability of hierarchically geared up structures, specifically structures of interacting behavioural phenotypes in animals and guy.

**Pulverized-Coal Combustion and Gasification: Theory and Applications for Continuous Flow Processes**

Viii and techniques will be tailored to different coal conversion and combustion difficulties, we haven't thought of combustion or gasification in fluidized or mounted beds or in situ tactics. furthermore, we haven't thought of different fossil-fuel combustion difficulties linked to oil shale, tar sands, and so on.

- Integrated Circuit Defect-Sensitivity: Theory and Computational Models
- Multiscale Methods in Quantum Mechanics: Theory and Experiment
- Landscapes Under Pressure: Theory and Practice of Cultural Heritage Research and Preservation
- Theory of Global Random Search

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

**Example text**

Problem 12. Is S(C) finite? 13) Smarandache primitive sequence A Smarandache sequence in which a term cannot be dived by any other ones. 44 Example: Smarandache prime-digital sequence, that is prime-digit numbers which are themselves prime: 2, 3, 5, 7, 23, 37, 53, ... [6] (ID=A019546) 14) Smarandache alternating series A series of the form ∑ (−1) k ⋅ a (k )−1 k where a(k) is any Smarandache sequence. As example the alternate series has been calculated for the Smarandache square-product sequence [4].

Problem 14. Is there any Smarandache sequence such that for a particular value of s, for instance s0 , Sb (s0 ) = K where K is the Catalan constant [5]? 47 18) Smarandache Mobius Function For any Smarandache sequence a(n) we can define the following function analogously to the Mobius function in number theory [5]: 0 Su(n)= - 1 (−1)k if a(n) has one or more repeated prime factors if a(n)=1 if a(n) is a product of k distinct primes Problem 15. For a given Smarandache sequence a(n) evaluate lim n→ ∞ ∑ n Su ( n) where s ∈ N ns Is there any Smarandache sequence a(n) such that its Smarandache Zeta function Sz(n) is related to this sum?

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?