[seqfan] Re: Another variation with a vertical cut

Neil Sloane njasloane at gmail.com
Sun Jul 6 19:50:02 CEST 2014


Eric's new version of this idea is now A244496.
Ready for checking and extending!

On Wed, Jul 2, 2014 at 11:27 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello SeqFans,
> Could someone please check? And comment -- if of interest?
> Many thanks! I guess this is a nice (?) variation on the
> recent https://oeis.org/A243357
>> Lexicographically earliest sequence with property that
>   if a vertical line is drawn between any pair of adjacent
>   digits p and q, the number Z formed by the p digits to
>   the left of the line is divisible by p.
>
> S = 1,2,3,11,5,6,4,8,12,13,15,21,22,24,17,16,25,19,7,23,27,...
>
> Example:
> a) draw a line between 6 and 4, for instance -- thus p = 6:
>    S = 1,2,3,11,5,6|,4,
> b) concatenate the last 6 digits before the line (to get Z):
>    Z = 231156
> c) Z/p is an integer (indeed, Z/6 = 38526)
>
> We have here (if I'm not wrong):
>
>          Z / p = integer   (Z ends in p and has digit-length p)
>          1 / 1 = 1
>         12 / 2 = 6
>        123 / 3 = 41
>          1 / 1 = 1
>          1 / 1 = 1
>      23115 / 5 = 4623
>     231156 / 6 = 38526
>       1564 / 4 = 391
>   23115648 / 8 = 2889456
>          1 / 1 = 1
>         12 / 2 = 6
>          1 / 1 = 1
>        213 / 3 = 71
>          1 / 1 = 1
>      21315 / 5 = 4263
>         52 / 2 = 26
>          1 / 1 = 1
>         12 / 2 = 6
>         22 / 2 = 11
>         22 / 2 = 11
>       2224 / 4 = 556
>          1 / 1 = 1
>    1222417 / 7 = 174631
>          1 / 1 = 1
>     241716 / 6 = 40286
>         62 / 2 = 31
>      71625 / 5 = 14325
>          1 / 1 = 1
> 417162519 / 9 = 46351391
>    1625197 / 7 = 232171
>         72 / 2 = 36
>        723 / 3 = 241
>         32 / 2 = 16
>    1972327 / 7 = 281761
> ...
>
> S is infinite, of course, as it can always be extended
> with an integer (not yet present) having only 1's.
>
> Best,
> É.
>
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



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