Five Little Pigs: A Hercule Poirot Mystery (Agatha Christie Collection). Agatha Christie

Five Little Pigs: A Hercule Poirot Mystery (Agatha Christie Collection)



Download Five Little Pigs: A Hercule Poirot Mystery (Agatha Christie Collection)



Five Little Pigs: A Hercule Poirot Mystery (Agatha Christie Collection) Agatha Christie ebook fb2
Publisher: Black Dog & Leventhal Publishers
Language: English
Page: 256
ISBN: 1579127347, 9781579127343

This book contains ten small chapters on various Smarandache-type sequences or numbers. The Smarandache function $S(n)$ is the smallest positive integer which divides $n!$. The pseudo-Smarandache function $Z(n)$ is the least positive integer for which $1+ 2+\cdots+ Z(n)$ is divisible by $n$; the Smarandache partial perfect sequence $(a_n)$ is defined by $a_1= a_2= 1$, $a_{2k+1}= a_{k+1}-1$, $a_{2k+2}= a_{k+1}+ 1$ $(k\ge 1)$, etc. Among others it is shown e.g. that the alternating iteration $Z(\cdots (\varphi(Z(\varphi(n))\cdots)$ ultimately leads to one of the following five $2$-cycles: 2-3, 8-15, 128-255, 32768-65535, 2147483648-4294967295. The sequence $(a_n)$ is neither periodic nor convergent. There are 481 solutions to the equation $S(n)+ S(n+1)= S(n+2)+ S(n+ 3)$ for $n\le 10^8$, and the auther conjectures there are infinitely many such solutions. A similar equation is $S(n)- S(n+1)= S(n+2)- S(n+ 3)$, having 422 solutions of the above type. Other problems studied include Smarandache continued fractions, sums of consecutive integers, concatenation, or deconcatenation problems. [ József Sándor (Cluj-Napoca) ] --Zbl 1040.11001 (Germany)



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