What are the next two numbers in this sequence?
2, 5, 13, 31, 61, 109, ??, ??
(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.
Puzzle Solution
