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A176705 Number of semiprimes between single (or isolated or non-twin) prime(n) and single (or isolated or non-twin) prime(n+1). 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 (list; graph; refs; listen; history; text; internal format)
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

Contribution 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

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Last modified November 21 17:44 EST 2017. Contains 295004 sequences.