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User:Peter Polm
I got intrigued by the Fibonacci Sequence Binary Plot.
See: http://mathworld.wolfram.com/FibonacciNumber.html
The binary representation of F(2^n+2^(n+1)) ends in n+2 zeroes.
So F(96) ends in 7 zeroes.
I wondered when maximum values of repeating zeroes/ones would occur.
Well: F(42) = 267914296 = 1111 1111 1000 0000 1100 0011 1000
has 7 repeating zeroes (and 9 repeating ones).
For increasing repeating zeroes I found:
F(3) 1 , F(6) 3, F(12) 4, F(19) 5, ...
The sequence for increasing repeating zeroes in increasing Fibonacci numbers:
3,6,12,19,38,42,68,243,384,515,740,1709,5151,11049,45641, ....
The sequence for increasing repeating ones:
1,4,10,14,23,42,125,148,272,336,373,484,717,1674,3911,17554, ....
Both are new, useful?
See: http://bigintegers.blogspot.com/p/index.html
Also made a plot up to F(5400), 100 cm * 70 cm, title:
Fibonacci Sequence(0-5400) Binary Plot
Leonardo Pisano(~1175~1250)
Ed Pegg Jr.(2003)
Peter Polm(2012)
If you're interested: PeterPolm(AT)yahoo(DOT)com