[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.
>
>
>
>
>
>
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>
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--
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.
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