On a Deconcatenation Problem

In a recent study of the PrimaIity oj the Smarandache Symmetric Sequences Sabin and Tatiana Tabirca observed a very high frequency of the prime factor 333667 in the factorization of the terms of the second order sequence. The question if this prime factor occurs peridically was raised. The odd behaviour of this and a few other primefadors of this sequence will be explained and details of the periodic occurence of this and of several other prime factors will be given

Base Solution

Definition of the Smarandache function S(n): S(n) = the smallest positive integer such that S(n)! is divisible by n

The Florentin Smarandache Function S(n)

A program SMARAND has been designed to generate S(n) up to a preset limit N (N up to 1000000 has been used in some applications)

On a Smarandache Partial Perfect Additive Sequence

It is shown that the sequence has an amusing oscillating behavior and that there are terms that approach for a certain type of large indices

An Integer as a Sum of Consecutive Integers

This is a simple study of expressions of positive integers as sums of consecutive integers. In the first part proof is given for the fact that N can ben expressed in exactly d(L)-1 ways as a sum of consecutive integers, L is the largest odd factor of N and d(L) is the number of divisors of L. In the second part answer is given to the question: Which is the smallest integer that can be expressed as a sum of consecutive integers in n ways

A brief account on Smarandache 2-2 subtractive relationships

This brief note on Smarandache 2-2 subtractive relationships should be seen in relation to the article on Smarandache k-k additive relationships in this issue of SNJ

Mainly Natural Numbers

A few elementary studies on Smarandache sequences and other number problems

Mainly Natural Numbers

sequences and other number problem

On A Concatenation Problem

This article has been inspired by questions asked by Charles Ashbacher in the Journal of Recreational Mathematics, vol. 29.2 It concerns the Smarandache Deconstructive Sequence. This sequence is a special case of a more general concatenated and sequencing procedure which is the subject of this study. Answers are given to the above questions