It's a multi-layered pattern

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The first 19 numbers of a sequence are

10 , 10 , 11 , 12 , 15 , 16 , 21 , 21 , 23 , 27 , 27 , 2 A , 2 D , 2 D , 2 F , 32 , 35 , 34 , 37 10, 10, 11, 12, 15, 16, 21, 21, 23, 27, 27, 2A, 2D, 2D, 2F, 32, 35, 34, 37

Find the 20th term.

The first number is in binary.


The answer is 38.

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1 solution

Sharky Kesa
May 15, 2015

The pattern was a sequence of prime numbers but put into a base, which was their term number plus one. So, 2 became 10, 3 became 10, 5 became 11 and so forth.

Thus, we want to find the 20th prime number, which is 71. 71 in base 21 is 38. Therefore, the answer is 38.

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