A114414 - OEIS

%I #10 Jul 13 2015 21:05:56

%S 8,12,14,21,28

%N Records in 4-almost prime gaps ordered by merit.

%C Next term (if it exists) associated with A014613 > 1030000. - _R. J. Mathar_, Mar 13 2007

%F a(n) = records in A114404/log(A014613)) = records in (A014613(n+1) - A014613(n))/log(A014613)).

%e Records defined in terms of A114404 and A014613

%e n A114404(n) A114404(n)/log(A014613(n)).

%e 1 8 8/log16 = 6.64385619

%e 2 12 12/log24 = 8.6943213

%e 3 4 4/log 36 = 2.57019442

%e 4 14 14/log40 = 8.73874891

%e 5 2 2/log54 = 1.15447195

%e 6 4 4/log 56 = 2.2880834

%e 7 21 21/log 60 = 11.810019

%e ...

%e 13 22 22/log 104 = 10.9071078

%e ...

%e 21 28 28/log 156 = 12.7671725

%p 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_, Mar 13 2007

%Y Cf. A014613, A065516, A111870, A111871, A114403-A114411, A114412-A114422.

%K nonn,more

%O 1,1

%A _Jonathan Vos Post_, Nov 25 2005