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 Funky Fibonacci Fractions (Posted on 2007-02-22)
100/89= 1.1235..., which includes the first five Fibonacci numbers.

10000/9899=1.010203050813213455... includes the first ten Fibonacci numbers.

1000000/998999=1.001002003005... produces the first 15 Fibonacci numbers.

If you add two zeros in the numerator and two nines (one at the beginning, one at the end) in the denominator, does this Fibonacci production go on?

 See The Solution Submitted by Old Original Oskar! Rating: 4.6667 (3 votes)

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 Unsatisfying answer (spoiler...sort of) | Comment 1 of 5
The following program verifies that at the next step, indeed the 1- through 4-digit Fibonaccis continue, until 6765 is converted to 6766 by a carry from the next, 5-digit, Fibonacci:

list
10   print 100000000/99989999
20   A=1:B=1
30   repeat
40     C=A+B:A=B:B=C:print C
50   until C>9999
OK
run
1.00010002000300050008001300210034005500890144023303770610098715972584418167660
9477713866163755036
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
2584
4181
6765
10946
OK

But I'm sure we all want to know why.

 Posted by Charlie on 2007-02-22 16:02:20

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