up to fib(258), at least one of fib(k) .. fib(k+6) is squareful.
Every sixth Fibonacci number is divisible by F_6 = 8 since the Fibonacci numbers are a strong divisibility sequence, so this will always hold. Charles Greathouse Analyst/Programmer Case Western Reserve University On Sun, Jul 15, 2012 at 4:00 PM, Wouter Meeussen <wouter.meeussen@telenet.be> wrote:
[[ apart from the fact that any fib(n) containing a factor p^i (i>1 of course) seems to have mod(n,p)=0 ]]
up to fib(258), at least one of fib(k) .. fib(k+6) is squareful. Analogously, the squareful fibs are spaced no more than 6 apart. Anyone for a counter-example?
Their separations are counted as {1, 5 times}, {2, 11 times}, {3, 5}, {4, 7}, {5, 4}, {6, 27} So 6 is a ‘preferred distance’ for lowish n.
Wouter
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