[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
>> 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
>>
>>
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
More information about the SeqFan
mailing list