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%I #20 May 07 2021 20:33:24
%S 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,
%T 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,
%U 3,2,1,1,4,2,18,6,2,4,3,7,1,5,5,2,9,2,1
%N Triprime gaps. First differences of A014612.
%H T. D. Noe, <a href="/A114403/b114403.txt">Table of n, a(n) for n=1..10000</a>
%F a(n) = A014612(n+1) - A014612(n).
%e a(1) = 4 = 12-8 where 8 is the first triprime and 12 is the second.
%e a(2) = 6 = 18-12
%e a(3) = 2 = 20-18
%e a(4) = 7 = 27-20
%p 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
%t Differences[Select[Range[425], PrimeOmega[#] == 3 &]] (* _Jayanta Basu_, Jul 01 2013 *)
%Y Cf. A014612, A065516, A111870, A111871, A114403-A114411, A114412-A114422.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Nov 25 2005
%E Corrected and extended by _R. J. Mathar_, Apr 25 2006
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