[seqfan] Re: A Sequential Puzzle

[charliemath at optonline.net]

In case any SeqFan is still looking for the answer to The Missing 
Element puzzle, read no further.


However, this answer just appeared (about 2PM, 3/26/18) in the Comments 
Section of the Wall St. Journal's Varsity Math Column:


"Tony Murphy 
Missing element:



A function interpolating all of the given points is 120*(2^M-1)/M where 
M=-3, -2, -1, (0), 1, 2 ... corresponds to 35,45,60,(q),120,180... etc.



For continuity, q has to be the limit as M-->0 of this function, where 
of course the formula doesn't work at M=0. This limit is easily 
calculated as 120*ln(2), or approx 83.178.





I guess the surprise is that q is not an integer in this case.




The above solution can be derived by looking at M*Given numbers and 
fiddling around with the resulting difference equation."


Note how close Tony's answer is to Olivier's (83 1/6) gotten by 
interpolation.


On Sat, Mar 24, 2018 at 10:21 AM, charliemath at optonline.net wrote:

> Some SeqFans may already be acquainted with a weekly column  entitled 
> Varsity Math, published Saturdays in the Wall St. Journal's Review 
> section. 
>
>
> The second ot two problems in today's edition is called The Missing 
> Element and reads as follows:
>
>
> The open-ended sequence ...35,45, 60, q, 120,180,280, 450, 744, 
> 1260,... has an undisclosed element, q.  Find a simple continuous 
> function to generate the sequence and compute the surprise answer for 
> q.
>
>
> I did a search for any sequence that contains 35 45 60 120 180 280 450 
> 744 1260.
> Seqence A103252 contains each value except 744.  No sequence contains 
> all 9 values.
>
>
> I'm guessing this sequence, once found, will make its way into OEIS.
>
>
> Enjoy!
>
>
> Charlie Marion
>
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>