%I A114414
%S A114414 8,12,14,21,28
%N A114414 Records in 4-almost prime gaps ordered by merit.
%C A114414 Next term (if it exists) associated with A014613 > 1030000. - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Mar 13 2007
%F A114414 a(n) = records in A114404/log(A014613)) = records in (A014613(n+1) - 
               A014613(n))/log(A014613)).
%e A114414 Records defined in terms of A114404 and A014613
%e A114414 n A114404(n) A114404(n)/log(A014613(n)).
%e A114414 1 8 8/log16 = 6.64385619
%e A114414 2 12 12/log24 = 8.6943213
%e A114414 3 4 4/log 36 = 2.57019442
%e A114414 4 14 14/log40 = 8.73874891
%e A114414 5 2 2/log54 = 1.15447195
%e A114414 6 4 4/log 56 = 2.2880834
%e A114414 7 21 21/log 60 = 11.810019
%e A114414 ...
%e A114414 13 22 22/log 104 = 10.9071078
%e A114414 ...
%e A114414 21 28 28/log 156 = 12.7671725
%p A114414 Digits := 16 : A114414 := proc() local n,a014613,a114414,rec ; a014613 
               := 16 ; a114414 := 8 ; rec := a114414/log(a014613) ; print(a114414) 
               ; n := 17 ; while true do while numtheory[bigomega](n) <> 4 do n 
               := n+1 ; od ; a114414 := n-a014613 ; if ( evalf(a114414/log(a014613)) 
               > evalf(rec) ) then rec := a114414/log(a014613) ; print(a114414) 
               ; fi ; a014613 := n ; n := n+1 : od ; end: A114414() ; - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Mar 13 2007
%Y A114414 Cf. A014613, A065516, A111870, A111871, A114403-A114411, A114412-A114422.
%Y A114414 Sequence in context: A106669 A108979 A107071 this_sequence A032455 A050275 
               A033949
%Y A114414 Adjacent sequences: A114411 A114412 A114413 this_sequence A114415 A114416 
               A114417
%K A114414 easy,nonn,more
%O A114414 1,1
%A A114414 Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 25 2005