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

0, 9, 19, 22, 27, 34, 42, 37, 42, 41, 50, 50, 53, 64, 69, 49, 54, 79, 90, 72, 86, 82, 87, 74, 86, 90, 96, 106, 111, 98, 103, 102, 107, 88, 91, 88, 95, 73, 80, 73, 76, 22, 29, 26, 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

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 06 2009

Keywords

• nonn

Examples

			a(1)=0 (3 > [none] > 2);
a(2)=9 (5 < 8,9,10,14,15,16,20,21,22 < 23);
a(3)=19 (7 < 8,9,10,14,15,16,20,21,22,24,25,26,27,28,32,33,34,35,36 < 37).
		

Crossrefs

Cf. A001097 (the nonisolated primes), A007510 (the isolated primes), A164276 (the nonisolated nonprimes), A167511.

Programs

Maple

isA001097 := proc(n) isprime(n) and ( isprime(n+2) or isprime(n-2) ); end proc:
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:
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:
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:
seq(A167529(n),n=1..120) ; # R. J. Mathar, May 30 2010

Extensions

Corrected (23 replaced with 22, 28 with 27) and extended by R. J. Mathar, May 30 2010