# [seqfan] Re: An "add or make the absolute difference" array

Eric Angelini Eric.Angelini at kntv.be
Wed Feb 15 23:46:56 CET 2012

```Hello Graeme,
22 is already in the array, thus no difference allowed there
Best,
É.

Le 15 févr. 2012 à 19:14, "Graeme McRae" <g_m at mcraefamily.com> a écrit :

> Eric, why does the fifth row not end with 22?
>
> --Graeme McRae,
> Palmdale, CA
>
> On Feb 15, 2012, at 6:22 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
>> Hello SeqFans,
>> could someone check and extend this seq (if of interest)?
>> [Requires lots of memory]
>>
>> S = 1, 2, 4, 7, 8, 10, 13, 12, 16, 20, 19, ...
>>
>> The idea:
>> - to put all the Naturals in an array, exactly once.
>> The array rule:
>> - if you take 2 neighboring integers anywhere in the array,
>> their sum or their absolute difference is on the line below,
>> between them.
>> The construction:
>> - Start the uppermost row with "1"
>> - extend the uppermost row with the "smallest integer not yet
>> checking first if the absolute difference between the new
>> integer and its left neighbor is not yet present in the array
>> -- else checking if the new integer can be added to its left
>> neighbor with no subsequent "damage" either (the result --
>> subtraction or addition -- will be written on the line below,
>> between the two integers, starting an anti-diagonal)
>> - complete the said anti-diagonal in the same way, then extend
>> the uppermost row with a new integer.
>>
>> 1 2  4   7    8    10    13    12    16    20  19
>> 3 6   11  15   18    23    25    28    36   39
>> 9  5   26  33    41    48    53    64    75
>>  14  21  59   74    89    101   117   139
>>    35  38  133   163   190   218   256
>>      73  95   30    353   408   474
>>        22  65    323    55   66
>>          43   258   268   121
>>            215   526   147
>> Best,           311   379
>> É.                 68
>>
>>
>>
>>
>>
>> _______________________________________________
>>
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>
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>
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```