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

Maximilian Hasler maximilian.hasler at gmail.com
Tue Jan 8 18:25:28 CET 2013

```note that e.g. row 12 ends ...,129, 1200.

Maximilian

On Tue, Jan 8, 2013 at 1:12 PM, Harvey P. Dale <hpd at hpdale.org> wrote:
>         Suppose my prior suggested Mma program is wrapped in "DeleteDuplicates":
>
>         DeleteDuplicates[Flatten[Table[{n,Range[10n,10n+n-2]},{n,20}]]]
>
> If that doesn't work properly, please let me know where and in what way it fails.
>
>         Best,
>
>         Harvey
>
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Charles Greathouse
> Sent: Monday, January 07, 2013 11:29 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: In search of a formula for a number triangle
>
> The Mathematica code is not correct, it allows repetitions but the definition does not. The sequence is indeed a rearrangement of the positive integers.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
>
> 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:
>>
>> 20,30,31,40,41,42,50,51,52,53,60,61,62,63,64,70,71,72,73,74,75,80,81,8
>> 2,83,8
>> 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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```