1, 4, 16, 25 are all square numbers: 1^2, 2^2, 4^2, 5^2
1+1=2, 2+2=4, 4+1=5. I guess the next basis number is 5+2=7 (+1,+2,+1,+2,+1,...)
So I would guess: 1 4 16 25 49 64 100 121 ...
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This is the series of square numbers, (16= 4*4). The next number is 5*5=25.
33
The Pattern is 1^2- 2^2- 3^2- 4^2- 5^2 or 1 - 4 - 9 - 16 - 25 The next number in the series is 6^2 or 36
49 (it is an arithmetic series that adds 5 then 7 then 9 then 11 then 13)
The next number is 25 but there are the sequence is infinite so there can be no end to the sequence.