Complete the following sequence: \begin{align} 0 \quad&\quad 1&2&\quad\quad3&4&\quad\quad5&6&\quad\quad7&8\\ \hline\\ 1\quad&\quad3&7&\quad\quad12&23&\quad\quad40&74&\quad\quad139&?\\ \end{align} Hints

  • It is a positive integer number.
  • $\begingroup$ Oh, come on! Still 1 answer ? I really don't wanna answer my own question. The pattern isn't hard to find if you look the numbers closely. Well maybe just a bit :) $\endgroup$ – Kitiara Aug 23 '17 at 18:59

My guess:



Look at the differences between the numbers:

2,4, 5,11, 17,34, 65,...

They seem to come in pairs, where the second one is twice the first one, or twice the first one plus one.
Continuing this pattern, the new difference must be 131, and the solution is 270.

  • $\begingroup$ 17 does not fit that pattern $\endgroup$ – paparazzo Aug 20 '17 at 19:32

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