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Extreme Fibonacci (Posted on 2023-12-15) Difficulty: 4 of 5
Given that a1=1, a2=5, an+1= (an * an-1)/(an2 + an-12 + 1)1/2. Find a expression of the general term of an.

No Solution Yet Submitted by Danish Ahmed Khan    
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re: Partial solution Comment 2 of 2 |
(In reply to Partial solution by Jer)

Something I noticed:

The denominators, without the square root, grow very fast.  The number of digits of these, at least for a while, are themselves fibonacci numbers.
1 (1 digit)
1 (1 digit)
27 (2 digits)
727 (3 digits)
54679 (5 digits)
85285383 (8 digits)
6529878175807 (13 digits)
6.33685E+20
4.24431E+33
2.69602E+54
1.14434E+88
3.08516E+142 (pattern ends here, not 144 digits)
3.53046E+230 (not 233 digits.  2 short.  Is the shortfall increasing?)
#NUM! (exceeds sheet's limit)

Here's my google sheet:

https://docs.google.com/spreadsheets/d/1rzt2a_iea0hxnTxOK4BnQMtBVE6l-6Tq2d9mSqItZKo/edit?usp=sharing

  Posted by Jer on 2023-12-15 15:54:04
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