# [seqfan] Re: Filling squares and triangles (with digits)

Neil Sloane njasloane at gmail.com
Wed Nov 27 02:19:20 CET 2013

```I think we should use both styles for both sequences,
so we will have four new sequences in all.

And I do like Eric's idea of filling a square
or a right triangle. I would like to see that as part
of the definition.

Otherwise we will be led to consider:

The integer k such that the numbers from 1 to k contain exactly A123456(n)
digits, or 0 if no such k exists,

where A123456 is any of the core sequences. Mentioning the square
in the definition makes it more interesting.

Best regards
Neil

On Tue, Nov 26, 2013 at 7:42 PM, <franktaw at netscape.net> wrote:

> Let me make one small correction to that. Instead of "You might mention it
> in a comment", read "You should mention it in a comment".
>
>
>
> -----Original Message-----
> From: franktaw <franktaw at netscape.net>
>
> If this becomes a sequence, I would recommend changing it to "The
> integer k such that the digits from 1 to k have exactly n^2 digits, or
> zero if this does not exist." So it would start:
>
> 1,4,9,0,17,0,29,...
>
> (I've also dropped the reference to "filling" squares - we're
> ultimately just counting digits here. Filling squares is the idea that
> got you here, but not the essence of what you've gotten to. You might
> mention it in a comment.)
>
> Don't forget to cross-reference A058183.
>
>
> -----Original Message-----
> From: Eric Angelini <Eric.Angelini at kntv.be>
> To: Sequence Discussion list <seqfan at list.seqfan.eu>
> Sent: Tue, Nov 26, 2013 6:08 pm
> Subject: [seqfan] Filling squares and triangles (with digits)
>
>
> Hello SeqFans,
> It is possible to write down in a 5 x 5
> square (25 cells)  the integers from 1
> to 17 -- if you use one digit per cell:
>
> 1 2 3 4 5
> 6 7 8 9 1
> 0 1 1 1 2
> 1 3 1 4 1
> 5 1 6 1 7
>
> The 4 x 4 square is impossible to fill
> exactly, using the same constraint:
>
> 1 2 3 4
> 5 6 7 8
> 9 1 0 1
> 1 1 2 1 3
>
> We see that 12 leaves an empty cell,
> and 13 needs one too much.
>
> What are the exact "square-filling" integers?
>
> I guess S starts:
> S=1,4,9,17,29,45,65,89,111,144,183,228,...
>
> The equivalent seq T could be constructed
> for exact "right-triangle-filling" integers:
>
> T=1,3,6,12,15,27,32,50,57,...
>
> None of those are in the
> O
> N L
> I N E
> E N C Y
> C L O P E
> D I A O F I
> N T E G E R S
> E Q U E N C E S
> Best,
> É.
> ----------
> (What about in other bases?)
>
>
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--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.