A126436 Number of composites between successive values of A014612.

2, 3, 0, 5, 0, 0, 8, 0, 0, 3, 1, 7, 2, 0, 1, 2, 0, 1, 10, 4, 0, 1, 1, 2, 2, 1, 0, 6, 0, 3, 5, 7, 0, 2, 0, 7, 0, 3, 0, 0, 0, 0, 4, 3, 1, 1, 2, 9, 3, 9, 4, 0, 3, 1, 1, 1, 0, 0, 7, 1, 2, 3, 1, 2, 1, 2, 1, 0, 0, 0, 3, 1

Offset: 1

Author

Jonathan Vos Post, Mar 12 2007

Keywords

• easy
• nonn

Examples

			a(1) = 2 because there are two composites {9,10} between A014612(1)=8 and A014612(2)=12.
a(2) = 3 because there are two composites {14, 15, 16} between A014612(2)=12 and A014612(3)=18.
a(3) = 0 because there are no composites between A014612(3)=18 and A014612(4)=20, only the prime 19.
a(7) = 8 because {32,33,34,35,36,38,39,40} between A014612(7)=30 and A014612(8)=42.
		

Crossrefs

3-almost prime analog of A046933 = number of composites between successive primes.

Cf. A002808, A014612, A046933, A070552, A114403.

Programs

Maple

isA014612 :=proc(n) if numtheory[bigomega](n) = 3 then true ; else false ; fi ; end: isA002808 := proc(n) RETURN(not isprime(n) and n <> 1 ); end: A126436 := proc(nmax) local a ; a := -1 ; for n from 1 to nmax do if isA014612(n) then if a >= 0 then printf("%d,",a) ; fi ; a := 0 ; elif isA002808(n) and a>= 0 then a := a+1 ; fi ; od : end: A126436(300) : # R. J. Mathar, Apr 03 2007

Mathematica

nmax = 72;
S = Select[Range[300](* increase range if a(n) unevaluated *), PrimeOmega[#] == 3&];
a[n_ /; n+1 <= Length[S]] := Count[Range[S[[n]]+1, S[[n+1]]-1], _?CompositeQ];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Oct 26 2023 *)

Formula

a(n) <= A114403(n) - 1.

Extensions

More terms from R. J. Mathar, Apr 03 2007