|
%I #11 Mar 13 2019 23:23:56
%S 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,
%T 38,39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,64,65,66,
%U 68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100,102,104
%N Composites of the form ((x+y)/3+2)/(x-y), where x=composite and y=prime.
%C x=c(i)=i-th composite and y=p(j)=j-th prime.
%C The current list of values may still be incomplete because it has been created combining the first 3500 composites and the first 2200 primes. [_R. J. Mathar_, Apr 25 2010]
%C This sequence is identical to A002808 (the composites): see link. - _Robert Israel_, Mar 13 2019
%H Robert Israel, <a href="/A140347/a140347.pdf">Proof that A140347 contains all composites</a>
%e If x=35 and y=31, then ((35+31)/3+2)/(35-31)=24/4=6=a(1).
%e If x=143 and y=139, then ((143+139)/3+2)/(143-139)=96/4=24=a(2).
%e If x=155 and y=151, then ((155+151)/3+2)/(155-151)=104/4=26=a(3).
%e If x=161 and y=157, then ((161+157)/3+2)/(161-157)=108/4=27=a(4).
%e If x=203 and y=199, then ((203+199)/3+2)/(203-199)=136/4=34=a(5).
%e If x=215 and y=211, then ((215+211)/3+2)/(215-211)=144/4=36=a(6),
%e etc.
%Y Cf. A002808, A000040.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Aug 28 2008
%E Many values (c=4 from (x=49,y=41), c=8 from (x=247,y=227), c=9 from (x=305,y=283), etc...) inserted by _R. J. Mathar_, Apr 25 2010
%E 38, 66, 76, 86, 90, 93 inserted by _Robert Israel_, Mar 13 2019
|
