[seqfan] Re: A108552 and iit's ratonal multiples!

[DAN_CYN_J]

Hi again all seqfans , 

  

Sequence A108552 -- 


1,8,180,1120,8064,604800,68428800,830269440,10897286400... 

  

The multiple of these sequential rationals below will make up the above sequence 
at certain points. At certain points in the sequential multiple it does not 
produce an integer but sets up the next rational in the multiple that produces 
an integer. 
The possible reason being that the formula states in A108552, 

 if n+1 is a composite at that  point only integers are produced. 
2*(n-1)!/(n+1)  where n+1 is a composite thus creating this 

sequence. 

Instead of the above formula to produce this sequence 

the rationals below are used as multiples in sequence. 

  

0+(2/3) =.6666666666666... 
1+(2/4) = 1.5 
2+(2/5) = 2.4 
3+(2/6) = 3.333333333333... 
4+(2/7) = 4.2857142857... 
5+(2/8) = 5.25 
6+(2/9) = 6.22222... 
7+(2/10) =7.2 
8+(2/11) =8.1818181818... 
9+(2/12) =9.1666666666... 
10+(2/13) =10.1538461538... 
11+(2/14) =11.1428571428... 
12+(2/15) =12.1333333333... 

and so-on ----> oo 


Where the gap between these rationals terms are always <1 but 
will eventually converge too (1). 



These are terms taken from the sequential list of rationals 

above and multiplied and when an integer ( =n) is produced  

  it is a term in the sequence A108552 

  
(0+(2/3)) * (1+(2/4)) =1 * (2+(2/5)) * (3+(2/6)) = 8 * (4+(2/7)) * (5+(2/8)) = 180 * (6+(2/9)) = 1120 * (7+(2/10)) =8064 ....etc. 

  

As you will note, some take more then one rational multiplied to arrive at the next integer 

but never more then two. 

  

Dan