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

1,6

Links

Table of n, a(n) for n=1..65.

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]

Example

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).

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)

Crossrefs

Cf. A007510, A014574, A164276.

Sequence in context: A270429 A359878 A270097 * A242398 A174112 A111490

Adjacent sequences: A167508 A167509 A167510 * A167512 A167513 A167514

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 05 2009

Extensions

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

Status

approved