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Great sequence (Posted on 2013-11-28) Difficulty: 4 of 5
2, 3, 5, 5, 8, 10, 12, 13, 17, 21, __...

No Solution Yet Submitted by Math Man    
Rating: 5.0000 (1 votes)

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pseudo-solution | Comment 1 of 3
This post has already a long life. 

Apparently it's easy. It seems like a Fibonacci sequence disturbed by another sequence. But then it has a 4D and went till now unsolved.

Now looking at it and with the taste of the MathMan puzzle of Terrific sequence, it occurs to me that there is a pseudosolution. 

Take the difference between two consecutive terms (1,2,0,3,2,2,1,4,4) and just find that sequence on pi digits. You find it at position 167,297,166. It doesn't occurs again in the first 200000000 digits of pi. 

The sequence goes: 12032214456...

It should be: 2, 2+1, 3+2, 5+0, 5+3, 8+2, 10+2, 12+1, 13+4, 17+4, 21+5, ... Next term then is 26.

But solution is unique only inside the first 200000000 digits. If you go ahead the sequence will (I'd bet) repeat and then....

Edited on May 17, 2016, 9:56 am
  Posted by armando on 2016-05-17 09:54:33

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