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

[Graeme McRae]

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
>  present in the array and not leading to a contradiction",
>  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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