Some results about four Smarandache U-product sequences

Some results about four Smarandache U-product sequences Felice Russo Micron Technology Italy Avezzano (Aq) Italy In this paper four Smarandache product sequences have been studied: Smarandache Square product sequence, Smarandache Cubic product sequence, Smarandache Factorial product sequence and Smarandache Palprime product sequence. In particular the number of primes, the convergence value for Smarandache Series, Smarandache Continued Fractions, Smarandache Infinite product of the mentioned sequences has been calculated utilizing the Ubasic software package. Moreover for the first time the notion of Smarandache Continued Radicals has been introduced. One conjecture about the number of primes contained in these sequences and new questions are posed too. Introduction In [1] Iacobescu describes the so called Smarandache U-product sequence. Let Un n ~ 1, be a positive integer sequence. Then a U-sequence is defined as follows: In this paper differently from [1], we will call this sequence a U-sequence of the first kind because we will introduce for the first time aU-sequence of the second kind defined as follows: In this paper we will discuss about the "Square product", "Cubic product", "Factorial product" and "Primorial product" sequences. In particular we will analyze the question posed by Iacobescu in [1] on the number of primes contained in those sequences. We will also analyze the convergence values of the Smarandache Series [2], Infinite product [3], Simple Continued Fractions [4] of the four sequences. Moreover for the first time we will introduce the notion of Smarandache Continued Radicals and we will analyse the convergence of sequences reported above.