EricD./0and1pattern

[Eric DESBIAUX]

 arf 
excuse me i made a mistake,
sum of 2 and 3 and i have the pattern
> >  010101
> >  001001
> >  sum of 3,4 (only, without 2) and i have the pattern
> >  010101010101
> >  001001001001
> >  000100010001
it's same than 2n+1

> Message du 21/03/08 04:21
> De : "Maximilian Hasler" 
> A : "Eric" 
> Copie à : 
> Objet : Re: EricD./0and1pattern
> 
> On Thu, Mar 20, 2008 at 8:03 PM, Eric  wrote:
> >  i make sum of 2 and 3 and i have the pattern
> >  010101
> >  001001
> >
> >  sum of 2,3,4 and i have the pattern
> >  010101010101
> >  001001001001
> >  000100010001
> >
> >  each time i have a pattern of a "n" numbers of columns (as width)
> >  and as length (6,12,30,42,56,...) A002378  Oblong (or pronic, or
> >  heteromecic) numbers: n(n+1)
> 
> not sure: I don't know exactly how your pattern is defined, but if it ends
> where every line has a 1 in the same position, it's not n x (n+1) but
> gcd(2,3,4...,n) (if you take all lines from 2 up to n ; if only 3 lines, then
> gcd( n-2, n-1, n), where "n" is the last, etc.)
> 
> note: 12 = 3x4, 30 = 5x6, but no 20 = 4x5 ? or 3x4x5 = 60 ?
> gives 30 a "1" in the end of line "4" ?
> 
> >  so n*n*(n+1)=n^3+n^2 which is A011379  n^2+n^3.
> 
> ??
> 
> >  for each pattern i consider the number of 0 and the number of 1,
> >  number of 0 | 7|23|55|107|194
> >  number of 1 | 5|13|25|43|58
> >  with A011379 as tool i can go faster
> 
> number of 0 = number of lines x number of columns - number of 1's
> 
> number of 1 = sum ( number of columns / "name" of each line )
> e.g.: 2x3 columns => 6 / 2 + 6 / 3 = 5 "1"s
>        3x4 columns => 12/2 + 12/3 + 12/4 = 13 "1"s
>        4x5 columns ? or 3x4x5 columns ?
>  then  60/2 + 60/3 + 60/4 + 60/5 "1"s !?
> 
> >  i make a search for 7|23|55|107|194...i have 6821 results
> >  i make a search for 5|13|25|43|58...i have 8528 results  lol :o)
> 
> I need to know a better definition of your construction:
> always from 2 up to the biggest number ?
> or only the last 3 lines ?
> 
> 
> >  PS : using the "|" caracter to separate numbers is not very efficient but i
> >  try it to test, and i'm surprised to see that the n integer sequence
> >  (1,2,3,4,5,6...) doesn't appear first in all cases...
> 
> using comma => find only sequences where these numbers are direct neighbors.
> using space => find everything having the given numbers anywhere (in
> the whole text)
> but I assume gives higher ranking if these numbers are
> (a) in the sequence rather than in the text
> (b) in the given order
> (c) early at the beginning of the sequence
> 
> Joyeuses Pâques,
> 
> Maximilian
> 
> 
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