Mainly Natural Numbers: A Few Elementary Studies on Smarandache Sequences and Other Number Problems

Henry Ibstedt

Jan 2003 · Infinite Study

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The author studies in ten chapters: the smallest integer that can be expressed as a sum of consecutive integers in a given number of ways, the alterating iterations of the Smarandache function and the Euler f-function, some large sequences, the Smarandache partial perfect additive sequence {having a very simple definition: a(1)=a(2)=1, a(2k+1)=a(k+1)-1, a(2k+2)=a(k+1)+1} which does not form loops and does not get a terminating value but an amusing oscillating behavior, the Smarandache general continued fractions (built with positive integer Smarandache sequences), the Smarandache k-k additive relationships and Smarandache 2-2 substractive relationships, some concatenation and deconcatenation problems (in particular a number of questions raised on the Smarandache deconstructive sequence are resolved).