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Why?

Why the dickens, not? 

Tuesday, March 08, 2005

The mystery of the ratios

prime(fibb(i)): i=0,1,2.....
sn = 2, 3, 3, 5, 7, 13, 23, 43, 79, 149, 263, 463, 829, 1481, 2593, 4507, 7817, 13477,23167, 39791, 67933,

Ratio:sn+1:sn
1.5,1.0,1.67,1.4,1.87,1.77,1.87,1.84,1.89,1.77,1.79,1.76,1.74,1.72,1.72,1.71

seemingly converges to 1.7

fibb(prime(i)):i=0,1,2........
1, 2, 5, 13, 89, 233, 1597, 4181, 28657, 514229, 1346269, 24157817, 165580141, 433494437

Ratio:sn+1:sn
2,2.5,2.6,6.85,2.62,6.85,2.62,6.85,17.94,2.62,17.94,6.85,2.62

2.62, 6.85, 17.94, make cyclic appearances. credit:sage

can't do a whole lot more with c++ data types, gets buggered in the 47th Fibonacci(long data type issue) and 10,000 oddth prime(static array limit issue). These can be overcome, ofcourse. To continue or not....

<ponders>
update: with my current 500GB machine, i can only go upto i=37(20 so far) for series 1 and i=27(13 so far) for series 2. unless i get a list...

urped by gumz @ 6:01 PM


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