Question about periodicity in Fibonacci numbers Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Fibonacci Numbers: Is This Notation Clear? How Can It Be Improved?Proof that Fibonacci Sequence modulo m is periodic?Number of zeros in Fibonacci sequences mod $p$Are there infinite Fibonacci primes if and only if there are infinite Fibonacci numbers that are Fibonacci pseudoprimes?Alternative “Fibonacci” sequences and ratio convergenceReverse and forward doubling identity in Fibonacci sequence $textmod 9$A question about Fibonacci numbers“Missing” numbers in Pisano period sequencesShow that $fracf_kn$ undergoes a cycle, where $M$ is the fractional part of $M$ and $f_k$ is the $k^textth$ Fibo numberQuasi-periodic sequence
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Question about periodicity in Fibonacci numbers
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Fibonacci Numbers: Is This Notation Clear? How Can It Be Improved?Proof that Fibonacci Sequence modulo m is periodic?Number of zeros in Fibonacci sequences mod $p$Are there infinite Fibonacci primes if and only if there are infinite Fibonacci numbers that are Fibonacci pseudoprimes?Alternative “Fibonacci” sequences and ratio convergenceReverse and forward doubling identity in Fibonacci sequence $textmod 9$A question about Fibonacci numbers“Missing” numbers in Pisano period sequencesShow that $fracf_kn$ undergoes a cycle, where $M$ is the fractional part of $M$ and $f_k$ is the $k^textth$ Fibo numberQuasi-periodic sequence
$begingroup$
This is related to Pisano periods, that is, the periods of the Fibonacci numbers modulo $k=2, 3, cdots$. I am studying the sequence $x(n+1)=b x(n)$ (here the brackets represent the fractional part function) with $b=(1+sqrt5)/2$ and $x(1) = 1/k, k=2, 3, cdots$. These sequences are also periodic.
I tried several values of $k$ and in all the cases both periods (Pisano periods and periods from my sequences) were identical. Is this a coincidence, or a well known result easy to prove? For the context, read my article on randomness theory, here. This fact is discussed in section 3.3.(b). My sequence is associated with the golden ratio numeration system, a well known numeration system with an irrational base.
calculus group-theory prime-numbers irrational-numbers fibonacci-numbers
asked Mar 27 at 17:11
Vincent GranvilleVincent Granville
798
$endgroup$
add a comment |
$begingroup$
This is related to Pisano periods, that is, the periods of the Fibonacci numbers modulo $k=2, 3, cdots$. I am studying the sequence $x(n+1)=b x(n)$ (here the brackets represent the fractional part function) with $b=(1+sqrt5)/2$ and $x(1) = 1/k, k=2, 3, cdots$. These sequences are also periodic.
I tried several values of $k$ and in all the cases both periods (Pisano periods and periods from my sequences) were identical. Is this a coincidence, or a well known result easy to prove? For the context, read my article on randomness theory, here. This fact is discussed in section 3.3.(b). My sequence is associated with the golden ratio numeration system, a well known numeration system with an irrational base.
calculus group-theory prime-numbers irrational-numbers fibonacci-numbers
asked Mar 27 at 17:11
Vincent GranvilleVincent Granville
798
$endgroup$
add a comment |
$begingroup$
This is related to Pisano periods, that is, the periods of the Fibonacci numbers modulo $k=2, 3, cdots$. I am studying the sequence $x(n+1)=b x(n)$ (here the brackets represent the fractional part function) with $b=(1+sqrt5)/2$ and $x(1) = 1/k, k=2, 3, cdots$. These sequences are also periodic.
I tried several values of $k$ and in all the cases both periods (Pisano periods and periods from my sequences) were identical. Is this a coincidence, or a well known result easy to prove? For the context, read my article on randomness theory, here. This fact is discussed in section 3.3.(b). My sequence is associated with the golden ratio numeration system, a well known numeration system with an irrational base.
calculus group-theory prime-numbers irrational-numbers fibonacci-numbers
asked Mar 27 at 17:11
Vincent GranvilleVincent Granville
798
$endgroup$
This is related to Pisano periods, that is, the periods of the Fibonacci numbers modulo $k=2, 3, cdots$. I am studying the sequence $x(n+1)=b x(n)$ (here the brackets represent the fractional part function) with $b=(1+sqrt5)/2$ and $x(1) = 1/k, k=2, 3, cdots$. These sequences are also periodic.
I tried several values of $k$ and in all the cases both periods (Pisano periods and periods from my sequences) were identical. Is this a coincidence, or a well known result easy to prove? For the context, read my article on randomness theory, here. This fact is discussed in section 3.3.(b). My sequence is associated with the golden ratio numeration system, a well known numeration system with an irrational base.
calculus group-theory prime-numbers irrational-numbers fibonacci-numbers
calculus group-theory prime-numbers irrational-numbers fibonacci-numbers
asked Mar 27 at 17:11
Vincent GranvilleVincent Granville
798
asked Mar 27 at 17:11
Vincent GranvilleVincent Granville
798
asked Mar 27 at 17:11
Vincent GranvilleVincent Granville
798
asked Mar 27 at 17:11
Vincent GranvilleVincent Granville
798
asked Mar 27 at 17:11
Vincent GranvilleVincent Granville
798
798
add a comment |
add a comment |
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