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