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

Harvey P. Dale hpd at hpdale.org
Tue Jan 8 18:57:12 CET 2013


	Union, unlike DeleteDuplicates, sorts the unique numbers and the sequence doesn't match that result.  But Maximilian correctly points out that my Mma program fails to "jump" properly at a(78) and fairly often thereafter.  What is needed is a modification of the Range parameter once the length of it exceeds 10.

	Best,

	Harvey
 

-----Original Message-----
From: zak seidov [mailto:zakseidov at yahoo.com] 
Sent: Tuesday, January 08, 2013 12:31 PM
To: Harvey P. Dale
Subject: Fw: [seqfan] Re: In search of a formula for a number triangle

Why not to use Union[..] io  DeleteDuplicates?
Best,
Zak


----- Forwarded Message -----
> From:  <hpd at hpdale.org>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Cc: 
> Sent: Tuesday, January 8, 2013 9:12 PM
> Subject: [seqfan] Re: In search of a formula for a number triangle
> 
>     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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