This Infinite Random Sequence?

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I was working on Random sequence and LCG's when I found this recursive algorithm:




$$X_n+1=[sqrtn(X_n+1)]%10$$




Where, $[x]$ is the floor function.



When executed with $X_0=0$, the sequence turns out to be:




0,0,1,2,5,9,5,4,5,9,8,0,1,6,4,1,1,2,9,6,0,0,1,1,2,1,5,3,4,2,0,0,1,5,0,4,8,8,1,3,8,0,1,9,5,7,7,0,7........




I tested it and found out that there is no repition in this sequence till $X_10000$

Is it a better alternative to LCG's?




sequences-and-series recurrence-relations recursion




share|cite|improve this question





















  • A quick test reveals that the mean of your sequence deviates significantly from $4.5$ (I stopped watching after $200times 10^6$ numbers $X_n,$ finally the mean values is about $4.19dots 4.21.$ What are your values?
    – gammatester
    Aug 6 at 9:46











  • i also got values around $4.405702381885952 $ at $10^8$ numbers
    – Maths textbook
    Aug 6 at 9:57










  • Also I get another sequence: $0,0,1,2,3dots$. $x_4$ is not $5$ because $x_4 = [sqrt3(2+1)] % 10 = 3$
    – gammatester
    Aug 6 at 10:09










  • Better in what sense? It isn't clear what you're asking.
    – Cameron Buie
    Aug 6 at 11:25














up vote
0
down vote

favorite












I was working on Random sequence and LCG's when I found this recursive algorithm:




$$X_n+1=[sqrtn(X_n+1)]%10$$




Where, $[x]$ is the floor function.



When executed with $X_0=0$, the sequence turns out to be:




0,0,1,2,5,9,5,4,5,9,8,0,1,6,4,1,1,2,9,6,0,0,1,1,2,1,5,3,4,2,0,0,1,5,0,4,8,8,1,3,8,0,1,9,5,7,7,0,7........




I tested it and found out that there is no repition in this sequence till $X_10000$

Is it a better alternative to LCG's?




sequences-and-series recurrence-relations recursion




share|cite|improve this question





















  • A quick test reveals that the mean of your sequence deviates significantly from $4.5$ (I stopped watching after $200times 10^6$ numbers $X_n,$ finally the mean values is about $4.19dots 4.21.$ What are your values?
    – gammatester
    Aug 6 at 9:46











  • i also got values around $4.405702381885952 $ at $10^8$ numbers
    – Maths textbook
    Aug 6 at 9:57










  • Also I get another sequence: $0,0,1,2,3dots$. $x_4$ is not $5$ because $x_4 = [sqrt3(2+1)] % 10 = 3$
    – gammatester
    Aug 6 at 10:09










  • Better in what sense? It isn't clear what you're asking.
    – Cameron Buie
    Aug 6 at 11:25












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I was working on Random sequence and LCG's when I found this recursive algorithm:




$$X_n+1=[sqrtn(X_n+1)]%10$$




Where, $[x]$ is the floor function.



When executed with $X_0=0$, the sequence turns out to be:




0,0,1,2,5,9,5,4,5,9,8,0,1,6,4,1,1,2,9,6,0,0,1,1,2,1,5,3,4,2,0,0,1,5,0,4,8,8,1,3,8,0,1,9,5,7,7,0,7........




I tested it and found out that there is no repition in this sequence till $X_10000$

Is it a better alternative to LCG's?




sequences-and-series recurrence-relations recursion




share|cite|improve this question













I was working on Random sequence and LCG's when I found this recursive algorithm:




$$X_n+1=[sqrtn(X_n+1)]%10$$




Where, $[x]$ is the floor function.



When executed with $X_0=0$, the sequence turns out to be:




0,0,1,2,5,9,5,4,5,9,8,0,1,6,4,1,1,2,9,6,0,0,1,1,2,1,5,3,4,2,0,0,1,5,0,4,8,8,1,3,8,0,1,9,5,7,7,0,7........




I tested it and found out that there is no repition in this sequence till $X_10000$

Is it a better alternative to LCG's?





sequences-and-series recurrence-relations recursion





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 6 at 11:22









Cameron Buie

83.5k771153




83.5k771153









asked Aug 6 at 9:21









Maths textbook

526




526











  • A quick test reveals that the mean of your sequence deviates significantly from $4.5$ (I stopped watching after $200times 10^6$ numbers $X_n,$ finally the mean values is about $4.19dots 4.21.$ What are your values?
    – gammatester
    Aug 6 at 9:46











  • i also got values around $4.405702381885952 $ at $10^8$ numbers
    – Maths textbook
    Aug 6 at 9:57










  • Also I get another sequence: $0,0,1,2,3dots$. $x_4$ is not $5$ because $x_4 = [sqrt3(2+1)] % 10 = 3$
    – gammatester
    Aug 6 at 10:09










  • Better in what sense? It isn't clear what you're asking.
    – Cameron Buie
    Aug 6 at 11:25
















  • A quick test reveals that the mean of your sequence deviates significantly from $4.5$ (I stopped watching after $200times 10^6$ numbers $X_n,$ finally the mean values is about $4.19dots 4.21.$ What are your values?
    – gammatester
    Aug 6 at 9:46











  • i also got values around $4.405702381885952 $ at $10^8$ numbers
    – Maths textbook
    Aug 6 at 9:57










  • Also I get another sequence: $0,0,1,2,3dots$. $x_4$ is not $5$ because $x_4 = [sqrt3(2+1)] % 10 = 3$
    – gammatester
    Aug 6 at 10:09










  • Better in what sense? It isn't clear what you're asking.
    – Cameron Buie
    Aug 6 at 11:25















A quick test reveals that the mean of your sequence deviates significantly from $4.5$ (I stopped watching after $200times 10^6$ numbers $X_n,$ finally the mean values is about $4.19dots 4.21.$ What are your values?
– gammatester
Aug 6 at 9:46





A quick test reveals that the mean of your sequence deviates significantly from $4.5$ (I stopped watching after $200times 10^6$ numbers $X_n,$ finally the mean values is about $4.19dots 4.21.$ What are your values?
– gammatester
Aug 6 at 9:46













i also got values around $4.405702381885952 $ at $10^8$ numbers
– Maths textbook
Aug 6 at 9:57




i also got values around $4.405702381885952 $ at $10^8$ numbers
– Maths textbook
Aug 6 at 9:57












Also I get another sequence: $0,0,1,2,3dots$. $x_4$ is not $5$ because $x_4 = [sqrt3(2+1)] % 10 = 3$
– gammatester
Aug 6 at 10:09




Also I get another sequence: $0,0,1,2,3dots$. $x_4$ is not $5$ because $x_4 = [sqrt3(2+1)] % 10 = 3$
– gammatester
Aug 6 at 10:09












Better in what sense? It isn't clear what you're asking.
– Cameron Buie
Aug 6 at 11:25




Better in what sense? It isn't clear what you're asking.
– Cameron Buie
Aug 6 at 11:25















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