A114414 Records in 4-almost prime gaps ordered by merit.

8, 12, 14, 21, 28

Offset

1,1

Comments

Next term (if it exists) associated with A014613 > 1030000. - R. J. Mathar, Mar 13 2007

Links

Table of n, a(n) for n=1..5.

Formula

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

Example

Records defined in terms of A114404 and A014613
n A114404(n) A114404(n)/log(A014613(n)).
1 8 8/log16 = 6.64385619
2 12 12/log24 = 8.6943213
3 4 4/log 36 = 2.57019442
4 14 14/log40 = 8.73874891
5 2 2/log54 = 1.15447195
6 4 4/log 56 = 2.2880834
7 21 21/log 60 = 11.810019
...
13 22 22/log 104 = 10.9071078
...
21 28 28/log 156 = 12.7671725

Maple

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

Crossrefs

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

Sequence in context: A329865 A108979 A107071 * A032455 A342809 A279963

Adjacent sequences: A114411 A114412 A114413 * A114415 A114416 A114417

Keyword

nonn,more

Author

Jonathan Vos Post, Nov 25 2005

Status

approved