Add to ORKG1. Let Sen) be the Smarandache function. In paper [1] it is proved the irrationality of i S(7). We note here that this result is contained in the following more general n=1 11. theorem (see e.g. [2]). Theorem 1 Let (xJ be a sequence of natural numbers with the properties: (1) there exists flo EN · such that xn ~ 11 for all 11 ~ flo; (2) x n < 17- I for an infinity of 11; a: ' X (3) xm> 0 for infinitely many m. Then the series L ~ is irrational. =1 n
We present a new proof of the irrationality of values of the series T<sub>q</sub>(z)= ∞/∑/n=0 z<sup>...
Abstract The Smarandache function S(n) is defined as the minimal positive integer m such that n|m!. ...
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the diviso...
have proved the irrationality of L-,-. n=l n. The author of this note [5] showed that this is a cons...
The Smarandache Irratioality Conjecture (see [lD claims: Conjecture. Let a(n) be the nth term of a S...
The studies concerning the series with Smarandache numbers have been done recently and represents an...
Abstract In this paper we prove some general results which imply, for example, the irrationality of ...
AbstractIn this paper we give irrationality results for numbers of the form ∑n=1∞ann! where the numb...
The main results of this paper give several criteria for certain infinite series of rational numbers...
The thesis deals with the irrationality, irrational sequences, linearly independent sums of series a...
In this paper we prove that all Smarandache concatenated k-power decimals are irrational numbers
AbstractThe study of irrationality properties of values of the generalized Tschakaloff series f(x) d...
We generalize a previous result due to Badea relating to the irrationality of some quick convergent ...
Denote by sigma(k)(n) the sum of the k-th powers of the divisors of n, and let S-k = Sigma(n >= 1) (...
The main result of this paper is a criterion for irrational sequences which consist of rational numb...
We present a new proof of the irrationality of values of the series T<sub>q</sub>(z)= ∞/∑/n=0 z<sup>...
Abstract The Smarandache function S(n) is defined as the minimal positive integer m such that n|m!. ...
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the diviso...
have proved the irrationality of L-,-. n=l n. The author of this note [5] showed that this is a cons...
The Smarandache Irratioality Conjecture (see [lD claims: Conjecture. Let a(n) be the nth term of a S...
The studies concerning the series with Smarandache numbers have been done recently and represents an...
Abstract In this paper we prove some general results which imply, for example, the irrationality of ...
AbstractIn this paper we give irrationality results for numbers of the form ∑n=1∞ann! where the numb...
The main results of this paper give several criteria for certain infinite series of rational numbers...
The thesis deals with the irrationality, irrational sequences, linearly independent sums of series a...
In this paper we prove that all Smarandache concatenated k-power decimals are irrational numbers
AbstractThe study of irrationality properties of values of the generalized Tschakaloff series f(x) d...
We generalize a previous result due to Badea relating to the irrationality of some quick convergent ...
Denote by sigma(k)(n) the sum of the k-th powers of the divisors of n, and let S-k = Sigma(n >= 1) (...
The main result of this paper is a criterion for irrational sequences which consist of rational numb...
We present a new proof of the irrationality of values of the series T<sub>q</sub>(z)= ∞/∑/n=0 z<sup>...
Abstract The Smarandache function S(n) is defined as the minimal positive integer m such that n|m!. ...
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the diviso...