# Find how this finite sequence completes

7 14 31 51 70 81 104 107 129 149 155 175 192 215 238 259 279

299 301 301 314 328 350 372

Inspired by the discussion with the author of, and the clues to its solution are in that discussion: What is the last integer in this sequence?

I have constructed a finite (terminating), non decreasing sequence (I purposefully allowed this and not strictly increasing) that has a unique solution.

Not only is the solution unique, but it has a strong personal meaning for me.

I first intended to give the solution here immediately, as I very much doubt that it will be found, part of the challenge is to find the reason it is the unique solution.

However before posting it, I decided to let it run for a while as an open question first.

• The text is very short. Are you sure I can uniquely decipher it without knowing the key? Mar 21 at 0:53
• Cryptograpy - because one element as the sequence was generated could be used in an encryption scheme. It means that finding the solution requires some lateral thinking. "I intended giving solution here" : Because when I drafted the post I presented the solution and asked if anyone could deduce the method. At the last moment I thought I'd see if anyone could actually complete the sequence, and I added references to the original question and my tentative answer there, as well as the discussion that followed. I did a mental calc last night, I am confident it is unique. Will justify ... Mar 21 at 13:13
• I've confirmed the uniqueness claim, within the limits of google. Will cross check with other search engines over next few days too. Mar 22 at 19:46
• Hi @bobble, Thanks for your explanations - I appreciate that. ~ ~ ~ ~ We can debate whether this puzzle does fall into the [cryptographic] category when I post the numeric completion, and then the reason why it is a unique solution. I think you might agree with me then. ~ ~ ~ ~ [[My login still fails - infinite loop of creating password then verifiying email address]] Mar 24 at 12:48
• I just checked with the other big 3 search engines, three find the means to identify the "larger strategy" I believe, but only one hit using one SE that finds the actual solution. This must be one of the harder puzzles, after finding the mechanics of the puzzle (this is not the hard part), you have to find the right search engine and the right "public key" (in a loose sense) to find the sequence completion. So that's a nice challenge - existence can be established a bit easier than to find the solution. A worthy puzzle as my ice breaker I hope. Mar 24 at 12:49