A167511 The count of isolated primes between n-th non-isolated nonprime and n-th isolated nonprime.

1, 1, 0, 0, 1, 2, 4, 5, 9, 9, 12, 11, 15, 15, 15, 17, 18, 21, 22, 24, 27, 36, 36, 40, 47, 51, 54, 55, 56, 58, 76, 76, 75, 77, 79, 96, 96, 97, 97, 99, 105, 114, 116, 117, 118, 119, 127, 130, 132, 132, 146, 147, 151, 151, 152, 159, 166, 166, 169, 169, 173, 176, 180, 180, 181

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 05 2009

Keywords

• nonn

Examples

			a(1)=1 (0<2<4); a(2)=1 (1<2<6); a(3)=0 (8<no<12); a(4)=0 (9<no<18); a(5)=1 ( 10<23<30); a(5)=2 (14<23&37<42); a(5)=4 (15<23&37&47&53<60).
		

Crossrefs

Cf. A007510, A014574, A164276.

Programs

Maple

Contribution from R. J. Mathar, Mar 18 2010: (Start)
isA007510 := proc(n) isprime(n) and not isprime(n+2) and not isprime(n-2) ; end proc:
isA001359 := proc(n) isprime(n) and isprime(n+2) ; end proc:
A001359 := proc(n) if n = 1 then 3 ; else for a from procname(n-1)+2 do if isA001359(a) then return a; end if; end do: end if: end proc:
isA164276 := proc(n) not isprime(n) and (not isprime(n-1) or not isprime(n+1)) ; end proc:
A164276 := proc(n) if n = 1 then 0; else for a from procname(n-1)+1 do if isA164276(a) then return a; end if; end do: end if: end proc:
A014574 := proc(n) A001359(n)+1 ; end proc:
A167511 := proc(n) a := 0 ; for i from A164276(n)+1 to A014574(n)-1 do if isA007510(i) then a :=a +1 ; end if; end do; a ; end proc:
seq(A167511(n),n=1..80) ; (End)

Formula

a(n) = #{ A007510(i): A164276(n) < A007510(i) < A014574(n)}. [From R. J. Mathar, Mar 18 2010]

a(n) = SUM{A010051(k)*(1-A164292(k)): A164276(n)<=k<=A014574(n)}. [From Reinhard Zumkeller, Apr 02 2010]

Extensions

a(12), a(31) and a(32) corrected by R. J. Mathar, Mar 18 2010