[seqfan] Re: A (new) problem

[Vladimir Shevelev]

Excellently, Max!

Thus values of k: 6,9,13,... one can call "non-essential"! Can you continue an interest sequence of
"non-essential" k?

Vladimir

----- Original Message -----
From: Max Alekseyev <maxale at gmail.com>
Date: Monday, April 26, 2010 10:35
Subject: [seqfan] Re: A (new) problem
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> On Sun, Apr 25, 2010 at 9:59 AM, Vladimir Shevelev 
> <shevelev at bgu.ac.il> wrote:
> 
> > Starting with set of the first 3 triangular numbers {0,1,3}, 
> we see that every nonnegative integer up to 4 is a sum of 2 
> triangular numbers, but 5 is not. With this moment we consider 
> union of  triangular numbers and squares (A054686). Further, we 
> see that every nonnegative integer up to 22 is a sum of 2 terms 
> of A054686, but 23 is not. With this moment we consider union of 
> A054686 and sequence of pentagonal numbers (A000326) and see 
>  that every  nonnegative integer up to 61 is a sum of 2 terms of 
> this union, but 62 is not. With this moment  we join sequence of 
> hexagonal numbers (A000384) etc. Thus we obtain sequence 5,23,62,...
> 
> Here are the terms below 10^7:
> 
> 5, 23, 62, 62, 723, 1578, 1578, 8139, 39644, 94323, 94323, 1317783,
> 1680515, 2025699, 3205598
> 
> Max
> 
> 
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 Shevelev Vladimir‎