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Euclid Squared (Posted on 2006-01-26) Difficulty: 3 of 5
What are the next two numbers in this sequence?

2, 5, 13, 31, 61, 109, ??, ??

See The Solution Submitted by Dan    
Rating: 4.0000 (2 votes)

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Solution Puzzle Solution Comment 4 of 4 |
(In reply to Answer by K Sengupta)

Denoting the ith term as T(i), let us denote the jth prime as P(j).

Then,

There are T(i+1) is precisely P(i) prime numbers away from T(i), for i>=1

Thus, T(2) = 5 is P(1) = 2 prime numbers away from T(1),
 
T(3) = 13 is P(2) = 3 prime numbers away from T(2),

Accordingly, T(7) would be P(6) = 11 prime numbers away from T(6) = 109

Therefore, T(7) = 181

T(8) would be P(7) = 13 prime numbers away from T(7) = 181

Therefore, T(7) = 277.

Consequently, the required missing terms are: 181 and 277.


  Posted by K Sengupta on 2008-11-20 07:03:56
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