[seqfan] Re: Array where a permutation of the primes produces all non-primes

[Maximilian Hasler]

Eric,

I have hastily created the entry
http://oeis.org/A203985
"Permutation of the primes such that successive absolute differences
yield all non prime numbers"

but we should add due credits for Jean-Marc's and Alexandre's work
(and also copy their terms (but I could not do this from the image)
- my code confirms their values so far,
but is too inefficient to get 60 terms quickly...)

Regards,

Maximilian



On Mon, Jan 9, 2012 at 9:23 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello SeqFans,
> Jean-Marc Falcoz has computed 60 terms of the first line hereunder,
> -- and the resulting array. The constraints were:
> 1) the first line of the array must be a permutation of the primes;
> 2) the array, seen as a whole, must be a permutation of the naturals;
> 3) any two neighboring integers have their absolute first difference
>   written on the line below, between them.
>
> 2  3   13  47   197   11  29   443  397   1321  4831   15559    211     5      19    41   293   113   971 ...
>  1  10  34  150  186   18  414   46   924   3510  10728   15348    206    14     22   252   180   858 ...
>    9  24  116  36   168  396  368  878   2586  7218    4620   15142    192     8    230   72   678 ...
>     15  92   80  132   228   28  510  1708   4632  2598   10522   14950    184   222   158  606 ...
>       77   12  52    96   200  482 1198  2924   2034   7924    4428   14766    38    64   448 ...
>          65  40   44   104  282  716  1726   890   5890    3496   10338   14728   26   384 ...
>            25   4    60   178  434 1010   836   5000   2394    6842   4390    14702  358 ...
>               21  56   118   256 576   174   4164   2606   4448   2452   10312   14344 ...
>                 35   62   138   320  402  3990  1558   1842    1996   7860    4032  ...
>                    27   76   182   82  3588  2432   284    154    5864    3828 ...
>                      49   106  100  3506  1156  2148    130    5710   2036 ...
>                         57   6   3406  2350   992   2018   5580   3674 ...
>                           51  3400  1056  1358  1026   3562   1906 ...
>                            3349   2344  302  332    2536  1656 ...
>                               1005   2042  30    2204   880 ...
>                                   1037  2012  2174  1324 ...
>                                      975   162   850 ...
>                                         813   688 ...
>                                            125 ...
>
> After 60 terms (first line), the smallest missing prime is 17 and
> the smallest missing non-prime is 39.
>
> The first line is the lexicographically first one, as the building
> method forced the next prime to be the smallest available one, not
> yet present and not leading to a contradiction.
>
> All odd non-primes are on the first descending diagonal from the left,
> and only there.
>
> Many thanks to Jean-Marc Falcoz for his computer skills, to Maximilian
> Hasler and Alexandre Wajnberg for their support.
>
> The full 60-lines array is visible there:
> http://www.cetteadressecomportecinquantesignes.com/PrimeArray.htm
>
> Best,
> É.
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/