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

1,2

Links

Table of n, a(n) for n=1..81.

Example

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).

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

Crossrefs

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

Sequence in context: A357773 A075981 A079368 * A357184 A228610 A106677

Adjacent sequences: A167526 A167527 A167528 * A167530 A167531 A167532

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 06 2009

Extensions

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

Status

approved