What number comes next in this sequence:
1 · 23 · 124 · 1251 · 26127 · 128129 · ?
Puzzle Copyright © Kevin Stone
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Answer
1301311 or 1210121.
Reasoning
Removing spaces from the original sequence gives:
1 23 124 1251 26127 128129
123124125126127128129
Now adding spaces back in, in the correct place:
123 124 125 126 127 128 129
The next few terms could be:
130 131 132
or
1210 1211 1212
Add these to the end:
123 124 125 126 127 128 129 130 131 132
or
123 124 125 126 127 128 129 1210 1211 1212
Remove the spaces again:
123124125126127128129130131132
or
123124125126127128129121012111212
Now break the sequence into chunks of increasing size:
1 23 124 1251 26127 128129 1301311
or
1 23 124 1251 26127 128129 1210121
So the missing term is 1301311 or 1210121.