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A167529 a(n) is the number of nonisolated nonprimes k such that (n-th nonisolated prime) < k < (n-th isolated prime).

%I A167529 #9 Feb 18 2019 16:56:17
%S A167529 0,9,19,22,27,34,42,37,42,41,50,50,53,64,69,49,54,79,90,72,86,82,87,
%T A167529 74,86,90,96,106,111,98,103,102,107,88,91,88,95,73,80,73,76,22,29,26,
%U A167529 37,21,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A167529 a(n) is the number of nonisolated nonprimes k such that (n-th nonisolated prime) < k < (n-th isolated prime).
%e A167529 a(1)=0 (3 > [none] > 2);
%e A167529 a(2)=9 (5 < 8,9,10,14,15,16,20,21,22 < 23);
%e A167529 a(3)=19 (7 < 8,9,10,14,15,16,20,21,22,24,25,26,27,28,32,33,34,35,36 < 37).
%p A167529 isA001097 := proc(n) isprime(n) and ( isprime(n+2) or isprime(n-2) ); end proc:
%p A167529 A001097 := proc(n) option remember; if n =1 then 3; else for a from procname(n-1)+2 by 2 do if isA001097(a) then return a; end if; end do: end if; end proc:
%p A167529 A007510 := proc(n) option remember; if n <= 2 then op(n,[2,23]) ; else for a from procname(n-1)+2 by 2 do if isprime(a) and not isprime(a+2) and not isprime(a-2) then return a; end if; end do: end if; end proc:
%p A167529 A167529 := proc(n) a := 0 ; for k from A001097(n)+1 to A007510(n)-1 do if isA164276(k) then a := a+1 ; end if; end do: a ; end proc:
%p A167529 seq(A167529(n),n=1..120) ; # _R. J. Mathar_, May 30 2010
%Y A167529 Cf. A001097 (the nonisolated primes), A007510 (the isolated primes), A164276 (the nonisolated nonprimes), A167511.
%K A167529 nonn
%O A167529 1,2
%A A167529 _Juri-Stepan Gerasimov_, Nov 06 2009
%E A167529 Corrected (23 replaced with 22, 28 with 27) and extended by _R. J. Mathar_, May 30 2010