Is everything part of a sequence?
November 8, 2009 am30 8:35 am
I wonder if there is a sequence 
(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 qbyte.org]
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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.
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), …
So we can write a polynomial such that f(0) = 1, f(1) = 2, f(2) = 87 (eg.
),
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…)
Hey, it was me who posted about A078511, not that I’d say that constituted finding a solution to your original problem!
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!
Jonathan
Kristen Told Me About Your iSte, NICE!,