A049535. Feb. 16-20, 5 consecutive dates containing a s

[Labos Elemer]

> Date sent:      Thu, 20 Feb 2003 09:21:31 -0700 (MST)
> From:           Richard Guy <rkg at cpsc.ucalgary.ca>
> To:             Don McDonald <parabola at paradise.net.nz>
> Copies to:      john.harper at mcs.vuw.ac.nz, <don.mcdonald at paradise.net.nz>,
>                 <seqfan at ext.jussieu.fr>
> Subject:        Re: A049535. Feb. 16-20, 5 consecutive dates containing a square.

> Two comments:
> 
>    (a) see Guy, Lacampagne & Selfridge, Primes
> at a glance, Math Comput 48(1987) 183-202;
> MR 87m:11008.
> 
>    (b) The terms `squareful' `powerful' (coined
> by Sol Golomb) should refer to cases where
> EVERY prime factor is at least squared.  What
> is meant here is `non-squarefree'. (is NJAS
> listening?)      R.
> 
> On Thu, 20 Feb 2003, Don McDonald wrote:
> 
> > seqfans, John H,  Greetings
> > 
> > Feb. 16th-20th ,2003, are 5 consecutive dates containing a square.
> > yyyy=2003  year
> > mm=02      month
> > dd=20.     date
> > 20.02.03  23:17
> > 
> > e.g. sequence A049535  extract below???
> > (3 of them contain a cube.)
> > 
> > 2003,02,15 = 5  307  13049
> > 20030216 = 2  2  2  17  31  4751   ** 2 cubed
> > 20030217 = 3  23  43  43  157      ** 43 squared
> > 20030218 = 2  13  13  19  3119      ** 13 squared  (helen t green?)
> > 20030219 = 11  11  11  101  149       ** 11 cubed
> > 20030220 = 2  2  3  3  3  5  7  7  757   ** 42 squared
> > 2003,02,21 = 619 ** 32359
> > 
> > 
> > (search sci.math 619 prime mercurial factorisation. mcdonald.)
> > = like  3 5 7 11 13 - 2 17 19 23 ??
> > 
> > :In article <Pine.GSO.3.96.980813170545.6488B-100000 at atlantis>,
> > :  "don <" <dsmcdona at actrix.gen.nz> wrote:
> > :
> > :> > A single partition of 619 proves it is prime below.
> > :> >
> > :> > Integer   619  = 15,249  -  14,630
> > :> >                = 3.13.17.23 - 2.5.7.11.19.
> > :> >
> > :> > Every prime factor beginning at 2 up to 23 appears on
> > :> > one side or the other of this special [partition] of 619,
> > :> > but never on both sides at once.
> > :> >
> > :> > Therefore, integer 619 is prime.
> > :> >          q.e.d.
> > 
> > don.mcdonald
> > my file > sa.MZD03.MZD03-Jan.Feb2003
> > 
> > Squarefree.squarerun :
> >     848 = 2^2 * N...            Square run 5
> >     1684 = 2^2 * N...           Square run 5
> >     2892 = 2^2 * N...           Square run 5
> >     3628 = 2^2 * N...           Square run 5
> >     5050 = 2  5^2*N..           Square run 5
> > 
> >   840 = 2^2 * N...            Square run 1
> >   841 = perfect square***29^2*N..
> >   844 = 2^2 * N...            Square run 1
> >   845 = 5  13^2*N..           Square run 2
> >   846 = 2  3^2*N..            Square run 3
> >   847 = 7  11^2*N..           Square run 4
> >   848 = 2^2 * N...            Square run 5
> > 
> > > Neil, Labos,
> > > Greeting.
> > > 
> > > Integer Sequences !
> > > Here is the A049535 entry in the table (this will take a moment): 
> > >  
> > > %I A049535 
> > > %S A049535 22020,24647,30923,47672,55447,57120,73447,74848,96675,105772,121667, 
> > > %T A049535 121847,152339,171348,179972,182347,185247,190447,200848,204323,215303, 
> > > %U A049535 217071,229172,233223,234375,240424,268223,274547,310120,327424,338920 
> > > %N A049535 Starts for strings of exactly (6 consecutive squareful numbers.)
> > > 
> > > comment. I believe this is an error / Definition should be
> > > Starts for strings of exactly... (6 consecutive /non-squarefree/ numbers.)
> > >
> > 
> > very first is ** 22020 all the 2s. (22 Feb.)
> > Don's amendment (non-squarefree) was probably accepted.
> > 
> > > regards,
> > > don.mcdonald at paradise.net.nz
> > > 06.11.02
> > 
> 
-----------------------------
Some weeks ago Don remarked this squarful versus non-squrefree 
terminology problem.
Previously I used name of "squareful" because the same was used in 
Eric Encyclopedia. I mentioned this to njas but not to Eric.
If zou use in Internet Lzcos kezword squareful,
still zou find this essentially incorrect or 
ambigous terminology.
Don was right and I agreed to replace with non-squrefree.

Still there is a weaker ambiguity:
non-square-free include squareful 
or not.
I think should include.

Yours 
Labos E.
Date=20030221 is not prime issquarefree