A114403 Triprime gaps. First differences of A014612.

4, 6, 2, 7, 1, 2, 12, 2, 1, 5, 2, 11, 3, 2, 2, 5, 1, 2, 14, 6, 1, 3, 3, 5, 4, 2, 1, 7, 1, 5, 8, 9, 1, 5, 1, 10, 1, 5, 1, 1, 2, 1, 7, 4, 2, 2, 5, 12, 5, 10, 8, 1, 5, 2, 4, 2, 1, 1, 9, 3, 3, 5, 2, 5, 2, 4, 3, 2, 1, 1, 4, 2, 18, 6, 2, 4, 3, 7, 1, 5, 5, 2, 9, 2, 1

Offset: 1

Author

Jonathan Vos Post, Nov 25 2005

Keywords

• easy
• nonn

Examples

			a(1) = 4 = 12-8 where 8 is the first triprime and 12 is the second.
a(2) = 6 = 18-12
a(3) = 2 = 20-18
a(4) = 7 = 27-20
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A014612, A065516, A111870, A111871, A114403-A114411, A114412-A114422.

Programs

Maple

is3Alm := proc(n::integer) local ifa,ex,i ; ifa := op(2,ifactors(n)) ; ex := 0 ; for i from 1 to nops(ifa) do ex := ex+ op(2,op(i,ifa)) ; od : if ex = 3 then RETURN(true) ; else RETURN(false) ; fi ; end: A014612 := proc(n::integer) local resul,i; i :=1; resul := 8 ; while i < n do resul := resul + 1 ; if is3Alm(resul) then i := i+1 ; fi ; od ; RETURN(resul) ; end: A114403 := proc(n::integer) RETURN(A014612(n+1)-A014612(n)) ; end: for n from 1 to 160 do printf("%d,",A114403(n)) ; od: # R. J. Mathar, Apr 25 2006

Mathematica

Differences[Select[Range[425], PrimeOmega[#] == 3 &]] (* Jayanta Basu, Jul 01 2013 *)

Formula

a(n) = A014612(n+1) - A014612(n).

Extensions

Corrected and extended by R. J. Mathar, Apr 25 2006