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

[Richard Guy]

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
>