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  • I generated the sequences mathematically in excel.
  • A Sequence N can be generated for any N>0 (I think it might be possible for N<0 but I'm not sure how that works. It would not be possible for N=0 because that makes no sense).

Sequence 1:

2,6,30,210,2310,30030,510510,9699690,223092870,6469693230,A

Sequence 2:

2,3,6,5,10,15,30,7,14,21,B

Sequence 3:

2,4,3,6,12,9,18,36,5,10,C

Sequence 4:

2,4,8,3,6,12,24,9,18,36,D

Sequence 5:

?,?,?,?,?

What are the values of A,B,C,D?

What is the beginning of Sequence 5?

Bonus Sequence for extra credit (generated in a similar way but doesn't fit in the Sequence N formula):

2,2,4,8,32,256,24,18,432,7776,?,?

Post Solution Edit (contains how I did it, don't read if you want to work it out yourself):

N is the number of distinct characters or base used for that sequence (N=2 is binary). I then just counted in that base and used the digits as the power values of a prime factorization. I didn't use Excel to calculate the primes, but I did use it to count in base N and do the prime un-factorization.

Here is a google doc that shows the method I used to calculate the sequences:

https://docs.google.com/spreadsheets/d/11ANRKXcuI02oiGIjyE8UOhQ03T0nAsqeOxI-5ykR3L8/edit?usp=sharing

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Here is a possible solution:

A = 200560490130 (the N-th term of the sequence is the product of the first N primes - I didn't know you could do this in Excel)
B = 42 (if you prepend 1, the pattern is 1*(1,2,3,6) 5*(1,2,3,6) 7*(1,2,3,6) - are you sure this shouldn't be 1,2,3,6,5,10,7,14 instead?
C = 20 (if you prepend 1, the pattern is 1*(1,2,4) 3*(1,2,4) 9*(1,2,4) 5*(1,2,4)
D = 72 (if you prepend 1, the pattern is 1*(1,2,4,8) 3*(1,2,4,8) 9*(1,2,4,8)
5 = 2,4,8,16,3 (continuing the pattern from C & D: 1*(1,2,4,8,16) 3*(1,2,4,8,16))

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  • $\begingroup$ You got the numbers I was expecting, but I think you went about it a different way. Isn't math great! I'll post an edit describing how I did it. $\endgroup$ – 182764125216 Aug 29 '16 at 13:35

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