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

%I A142338 #10 Nov 10 2020 03:23:01
%S A142338 1,6,12,15,16,20,24,27,33,39,42,45,45,50,52,54,55,63,63,66,70,70,70,
%T A142338 78,81,84,86,102,105,108,110,115,117,117,118,121,121,132,133,138,141,
%U A142338 146,148,150,156,158,165,168,168,171,180,180,182,198,203,205,205,210,210
%N A142338 Nonprimes of the form (p(2*n)-p(n))/4, where p(n)=n-th prime.
%C A142338 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
%H A142338 Robert Israel, <a href="/A142338/b142338.txt">Table of n, a(n) for n = 1..10000</a>
%e A142338 If n=2, then (p(2*2)-p(2))/4=(7-3)/4=1=a(1).
%e A142338 If n=6, then (p(2*6)-p(6))/4=(37-13)/4=6=a(2).
%e A142338 If n=11, then (p(2*11)-p(11))/4=(79-31)/4=12=a(3).
%e A142338 If n=13, then (p(2*13)-p(13))/4=(101-41)/4=15=a(4).
%e A142338 If n=14, then (p(2*14)-p(14))/4=(107-43)/4=16=a(5), etc.
%p A142338 q:= 1: p:= 1: count:= 0: R:= NULL:
%p A142338 while count < 100 do
%p A142338   q:= nextprime(q); p:= nextprime(nextprime(p));
%p A142338   v:= (p-q)/4;
%p A142338   if v::integer and not isprime(v) then count:= count+1; R:= R, v fi
%p A142338 od:
%p A142338 R; # _Robert Israel_, Nov 09 2020
%Y A142338 Cf. A000040, A072473, A141468.
%K A142338 nonn
%O A142338 1,2
%A A142338 _Juri-Stepan Gerasimov_, Sep 18 2008
%E A142338 59 and 87 removed by _R. J. Mathar_, Oct 04 2008