[seqfan] Re: New "knife" sequence

[Neil Sloane]

Followup to Eric June 26 "sister" to A243357. Eric said:
(start)
The « knife » sequence https://oeis.org/A243357
could have a « sister » one (where the digit dividing Z
is not the last one of Z but the digit immediately
to the right of the "cut".

> Lexicographically earliest sequence with property
that if a vertical line is drawn between any pair of
adjacent digits, the number Z formed by the digits
to the left of the line is divisible by the first
digit following Z.

The pattern of this new sequence is strange! (if I
did not make too many mistakes):

S = 1,11,3,7,71,31,111,113,33,117,331,1111,1311,1331,9,...
(end)
I guess we choose the next term, a(n), to be the minimal *number*
not already in the sequence, not containing any zero digits,
such that the property " if a vertical line is drawn between any pair of
adjacent digits, the number Z formed by the digits
to the left of the line is divisible by the first
digit following Z"
holds.
So even if Z is prime, the next term can start with a 1.
So if Z is divisible by d \in {2,3,...,9} the next term can
start with 1 or d, otherwise it must start with 1.
There is a question to be decided.
Are we trying to get the earliest string of DIGITS,
or the earliest string of NUMBERS. I say "NUMBERS",
otherwise we have to consider the possibility that a(n) = 11113...11
or some other long number would be better.

Then what I get is

1,11,3,7,x

Now 11137 = 7*37*43, so x starts with 1 or 7. Eric took x=71.
But a smaller legal x is 12, so we get
1,11,3,7,12 (?).  Ahah, Eric was right, x cannot be 12,
because 111371 is prime, so not divisible by 2.
So x is not 12, 13, ..., 19.
The next smallest x is 71, and this works.

This is very tricky. I will create an entry for this,
A244471, in the hope
that someone will program it and check it.

Neil






On Thu, Jun 26, 2014 at 1:44 PM, Eric Angelini <Eric.Angelini at kntv.be>
wrote:

>
> Hello SeqFans,
>
> The « knife » sequence https://oeis.org/A243357
> could have a « sister » one (where the digit dividing Z
> is not the last one of Z but the digit immediately
> to the right of the "cut".
>
> Definition:
>
> > Lexicographically earliest sequence with property
> that if a vertical line is drawn between any pair of
> adjacent digits, the number Z formed by the digits
> to the left of the line is divisible by the first
> digit following Z.
>
> The pattern of this new sequence is strange! (if I
> did not make too many mistakes):
>
> S = 1,11,3,7,71,31,111,113,33,117,331,1111,1311,1331,9,...
>
> 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