# [seqfan] Re: In search of a formula for a number triangle

Alonso Del Arte alonso.delarte at gmail.com
Tue Jan 8 02:34:11 CET 2013

```A077339 is a version of the triangle that does allow repetition, while
A077341 does not. Thus 20 does appear twice in A077339, but it should only
appear once in A077341.

At first I was skeptical all positive integers occur in A077341, but then I
remembered the frivolous theorem of arithmetic.

Al

On Mon, Jan 7, 2013 at 8:25 PM, Robert G. Wilson v <rgwv at rgwv.com> wrote:

> Seq.Fans,
>
> The statement "Every positive number appears exactly once" is incorrect, if
> the terms and the Mathematica coding are correctly presented. I find that
> the following terms appear twice:
>
> 20,30,31,40,41,42,50,51,52,53,60,61,62,63,64,70,71,72,73,74,75,80,81,82,83,8
> 4,85,86,90,91,92,93,94,95,96,97,...,.
> The following terms appear three
> times:130,140,141,150,151,152,160,161,162,163,...,.
> The following terms appear four times:
> 240,250,251,260,261,262,270,271,272,273,...,.
> The following terms appear five times:
> 350,360,361,370,371,372,380,381,382,383,...,. etc.
>
> Bob.
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Harvey P.
> Dale
> Sent: Monday, January 07, 2013 6:37 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: In search of a formula for a number triangle
>
> Al:
>
>         Does this Mma program properly generate the terms of the sequence?
>
>         Flatten[Table[{n,Range[10n,10n+n-2]},{n,20}]]
>
>         Best,
>
>         Harvey
>
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Alonso
> Del
> Arte
> Sent: Monday, January 07, 2013 5:40 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] In search of a formula for a number triangle
>
> The triangle of A077341
>
> 1
>
> 2 20
>
> 3 30 31
>
> 4 40 41 42
>
> 5 50 51 52 53
>
> ...
>
>  19 190 191 ...
>
> 200 201 202 ...
>
>  21 210 211 ...
>
> ...
>
> and the related sequence A077342, initial rows of the triangle, has the
> question "Can anyone derive a formula for a(n)?" I can't, but I believe I
> may at least be able to figure out which a(n) = n. This is what I've come
> up
> with:
>
> a(n) = n when n > 10 * floor(n/10) + floor(n/10) - 2.
>
> But of course this only takes into account the nearest previous row that
> could possibly contain n. Is that enough or does this formula need to be
> amended to take into account even earlier rows?
>
> Al
>
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--
Alonso del Arte
Author at SmashWords.com<https://www.smashwords.com/profile/view/AlonsoDelarte>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
```