Here is a cool sequence.

1,10,101,1020,10301,______,_______...

What numbers go in the two blanks?

(In reply to

Answer by K Sengupta)

Let the pth term of the sequence be S(p).

Then, the terms are given by the recursion relation:

S(p) = S(p-2) + 10*S(p-1)

Accordingly, we observe that:

S(3) = 1 + 10*10 = 101

S(4) = 10 + 10*101 = 1020

S(5) = 101 + 10*1020 = 10301

S(6) = 1020 + 10*10301 = 104030

S(7) = 10301 + 10*104030 = 1050601

Consequently, the missing 6th and 7th terms are respectively 104030 and 1050601