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Is everything part of a sequence?

November 8, 2009 am30 8:35 am

I wonder if there is a sequence n_1, n_2, n_3,... of n_i such that 1, 2, n does not appear in the On-Line Encyclopedia of Integer Sequences…

(Nickh, a math blogger, found the solution to an old problem I posed. Turns out, the answers form a known sequence)

[edited to point to the correct Nick – the puzzler at]

6 Comments leave one →
  1. November 8, 2009 am30 8:49 am 8:49 am

    If you plan to work on this, please note A087774 eliminates all numbers two more than a multiple of 3 (ie, 5, 8, 11,…) from consideration.

  2. November 8, 2009 pm30 12:02 pm 12:02 pm

    I don’t know if there is an interesting sequence with that property, but it certainly is true that for any finite list of numbers there is a polynomial f such that that list is the beginning of the sequence f(0), f(1), f(2), …

  3. November 8, 2009 pm30 12:14 pm 12:14 pm

    So we can write a polynomial such that f(0) = 1, f(1) = 2, f(2) = 87 (eg. f(x) = \frac{85}{2}x^2 + -\frac{83}{2}x + 1),

    but the OnLine Dictionary of Integer Sequences has nothing listed.

    So 87 comes first.

    (and yes, I manually checked 1 – 86. Can’t be the best way…)

  4. November 9, 2009 pm30 2:24 pm 2:24 pm

    Hey, it was me who posted about A078511, not that I’d say that constituted finding a solution to your original problem!

    • November 9, 2009 pm30 9:58 pm 9:58 pm

      Puzzle Nick! not worksheet Nick! I should have figured. He’s a nice guy, too.

      Didn’t I cheat you credit once before? I need to work on that. And I’ll go fix the post.

      In any case, thanks for the Sequence, and thanks for the heads up!


  5. November 20, 2009 am30 12:18 am 12:18 am

    Kristen Told Me About Your iSte, NICE!,

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