tags:

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 qbyte.org]

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!

Jonathan

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