A142338 Nonprimes of the form (p(2*n)-p(n))/4, where p(n)=n-th prime.

1, 6, 12, 15, 16, 20, 24, 27, 33, 39, 42, 45, 45, 50, 52, 54, 55, 63, 63, 66, 70, 70, 70, 78, 81, 84, 86, 102, 105, 108, 110, 115, 117, 117, 118, 121, 121, 132, 133, 138, 141, 146, 148, 150, 156, 158, 165, 168, 168, 171, 180, 180, 182, 198, 203, 205, 205, 210, 210

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 18 2008

Keywords

• nonn

Comments

Terms are in order of n. The sequence has repetitions and is not monotonic: e.g. a(71) = 249 and a(72) = 248. - Robert Israel, Nov 09 2020

Examples

			If n=2, then (p(2*2)-p(2))/4=(7-3)/4=1=a(1).
If n=6, then (p(2*6)-p(6))/4=(37-13)/4=6=a(2).
If n=11, then (p(2*11)-p(11))/4=(79-31)/4=12=a(3).
If n=13, then (p(2*13)-p(13))/4=(101-41)/4=15=a(4).
If n=14, then (p(2*14)-p(14))/4=(107-43)/4=16=a(5), etc.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A072473, A141468.

Programs

Maple

q:= 1: p:= 1: count:= 0: R:= NULL:
while count < 100 do
  q:= nextprime(q); p:= nextprime(nextprime(p));
  v:= (p-q)/4;
  if v::integer and not isprime(v) then count:= count+1; R:= R, v fi
od:
R; # Robert Israel, Nov 09 2020

Extensions

59 and 87 removed by R. J. Mathar, Oct 04 2008