A114415 Records in 5-almost prime gaps ordered by merit.

16, 24, 28, 42, 56, 70

Offset

1,1

Comments

Next term, if it exists, is associated with indices above 100000 in A114405 and A014614. - R. J. Mathar, May 10 2007

Links

Table of n, a(n) for n=1..6.

Formula

a(n) = records in A114405/log(A014614)) = records in (A014614(n+1) - A014614(n))/log(A014614)).

Example

Records defined in terms of A114405 and A014614
n A114405(n) A114405(n)/log(A014614(n)).
1 16 16/log 32 = 10.6301699
2 24 24/log 48 = 14.2751673
3 8 8/log 72 = 4.30725248
4 28 28/log 80 = 14.7129144
5 4 4/log 108 = 1.96712564
6 8 8/log 112 = 3.90392819
7 42 42/log 120 = 20.2002592
8 6 6/log 168 = 2.69625443
...
22 56 56/log 312 = 22.4524976

Maple

A014614 := proc(nmax) local a, i; a := [] ; i := 1 ; while nops(a) < nmax do if numtheory[bigomega](i) = 5 then a := [op(a), i] ; fi ; i := i+1 ; end: a ; end: A114405 := proc(a014614) local a, i; a := [] ; for i from 2 to nops(a014614) do a := [op(a), op(i, a014614)-op(i-1, a014614)] ; od ; a ; end: a014614 := A014614(100000) : a114405 := A114405(a014614) : Digits := 30 : rec := -1 : for i from 1 to nops(a114405) do if evalf(a114405[i]/log(a014614[i])) > rec then printf("%d, ", a114405[i]) ; rec := evalf(a114405[i]/log(a014614[i])) ; fi ; od ; # R. J. Mathar, May 10 2007

Crossrefs

Cf. A014614, A065516, A111870, A111871, A114403-A114411, A114412-A114422.

Sequence in context: A337378 A166319 A271783 * A320141 A225903 A033987

Adjacent sequences: A114412 A114413 A114414 * A114416 A114417 A114418

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 25 2005

Extensions

a(6) from R. J. Mathar, May 10 2007

Status

approved