A176705 Number of semiprimes between single (or isolated or non-twin) prime(n) and single (or isolated or non-twin) prime(n+1).

8, 5, 3, 2, 5, 3, 1, 3, 4, 2, 6, 1, 8, 3, 1, 1, 12, 7, 1, 4, 2, 2, 3, 4, 7, 2, 6, 2, 3, 2, 3, 1, 1, 2, 1, 4, 1, 2, 7, 0, 3, 3, 2, 4, 3, 1, 2, 2, 1, 12, 3, 3, 2, 3, 4, 2, 1, 1, 5, 3, 1, 5, 1, 2, 3, 5, 3, 3, 2, 1, 2, 0, 3, 2, 1, 3, 1, 4, 4, 11, 5, 1, 4, 3, 7, 0, 3, 4, 2, 1, 1, 2, 5, 0, 2, 2, 2, 2, 4, 1, 3, 9, 5, 1, 2

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Example

a(1)=8 because are 8 semiprimes (4, 6, 9, 10, 14, 15, 21, 22) between A007510(1)=2 and A007510(2)=23.

Maple

From R. J. Mathar, Apr 26 2010: (Start)
isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
A176705 := proc(n) a :=0 ; for k from A007510(n) to A007510(n+1) do if isA001358(k) then a := a+1 ; end if; end do: return a ; end proc:
seq(A176705(n), n=1..120) ; (End)

Mathematica

nsps[lst_]:=Module[{s=lst[[1]]+1, t=lst[[2]]-1}, Count[Range[s, t], _?(PrimeOmega[ #] == 2&)]]; With[{ip=DeleteCases[Prime[Range[200]], _?(AnyTrue[{#-2, #+2}, PrimeQ]&)]}, nsps/@Partition[ip, 2, 1]] (* The program uses the function AnyTrue from Mathematica version 10 *) (* Harvey P. Dale, Aug 13 2014 *)

Crossrefs

Cf. A001097, A007510.

Sequence in context: A196515 A116397 A275306 * A140133 A086723 A011406

Adjacent sequences: A176702 A176703 A176704 * A176706 A176707 A176708

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 24 2010

Extensions

a(4), a(13), a(55) corrected by R. J. Mathar, Apr 26 2010

Status

approved