%I #14 Jan 22 2025 02:31:57
%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(n)/log_10(A014613(n)) = records in (A014613(n+1) - A014613(n))/log_10(A014613(n)).
%e Records defined in terms of A114404 and A014613:
%e n A114404(n) A114404(n)/log_10(A014613(n))
%e = ========== =============================
%e 1 8 8/log_10(16) = 6.64385619
%e 2 12 12/log_10(24) = 8.6943213
%e 3 4 4/log_10(36) = 2.57019442
%e 4 14 14/log_10(40) = 8.73874891
%e 5 2 2/log_10(54) = 1.15447195
%e 6 4 4/log_10(56) = 2.2880834
%e 7 21 21/log_10(60) = 11.810019
%e ...
%e 13 22 22/log_10(104) = 10.9071078
%e ...
%e 21 28 28/log_10(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