# [seqfan] Re: A (new) problem

Mon Apr 26 10:05:38 CEST 2010

```Excellently, Max!

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

----- 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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