On a problem concerning the Smarandache Unary sequence

Abstract

In this paper a problem posed in [1J and concerning the number of primes in the Smarandache Unary sequence is analysed. Introduction In [1] the Smarandache Unary sequence is defined as the sequence obtained concatenating Pn digits of 1, where Pn is the n-th prime number: 11,111,11111,1111111,11111111111,1111111111111,11111111111111111, ......... . In the same paper the following open question is reported: How many terms in the Smarandache Unary sequence are prime numbers? In this paper we analyse that question and a conjecture on the number of primes belonging to the Smarandache Unary sequence is formulated. Results A computer program with Ubasic software package has been written to check the first 311 terms of the Unary sequence; we have found only five prime numbers. If we indicate the n-th term of the unary sequence as: 10Pn -1 u(n) =--9where Pn is the n-th prime.