A140347 Composites of the form ((x+y)/3+2)/(x-y), where x=composite and y=prime.

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 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

Offset

1,1

Comments

x=c(i)=i-th composite and y=p(j)=j-th prime.

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]

This sequence is identical to A002808 (the composites): see link. - Robert Israel, Mar 13 2019

Links

Table of n, a(n) for n=1..76.

Robert Israel, Proof that A140347 contains all composites

Example

If x=35 and y=31, then ((35+31)/3+2)/(35-31)=24/4=6=a(1).
If x=143 and y=139, then ((143+139)/3+2)/(143-139)=96/4=24=a(2).
If x=155 and y=151, then ((155+151)/3+2)/(155-151)=104/4=26=a(3).
If x=161 and y=157, then ((161+157)/3+2)/(161-157)=108/4=27=a(4).
If x=203 and y=199, then ((203+199)/3+2)/(203-199)=136/4=34=a(5).
If x=215 and y=211, then ((215+211)/3+2)/(215-211)=144/4=36=a(6),
etc.

Crossrefs

Cf. A002808, A000040.

Sequence in context: A002808 A018252 A141468 * A140209 A077091 A340268

Adjacent sequences: A140344 A140345 A140346 * A140348 A140349 A140350

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 28 2008

Extensions

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

38, 66, 76, 86, 90, 93 inserted by Robert Israel, Mar 13 2019

Status

approved