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

16, 24, 28, 42, 56, 70

Offset: 1

Author

Jonathan Vos Post, Nov 25 2005

Keywords

• easy
• nonn

Comments

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

Examples

			Records defined in terms of A114405 and A014614:
  n  A114405(n)  A114405(n)/log_10(A014614(n))
  =  ==========  =============================
  1      16      16/log_10(32)  = 10.6301699
  2      24      24/log_10(48)  = 14.2751673
  3      8       8/log_10(72)   = 4.30725248
  4      28      28/log_10(80)  = 14.7129144
  5      4       4/log_10(108)  = 1.96712564
  6      8       8/log_10(112)  = 3.90392819
  7      42      42/log_10(120) = 20.2002592
  8      6       6/log_10(168)  = 2.69625443
  ...
  22     56      56/log_10(312) = 22.4524976
		

Crossrefs

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

Programs

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

Formula

a(n) = records in A114405(n)/log_10(A014614(n)) = records in (A014614(n+1) - A014614(n))/log_10(A014614(n)).

Extensions

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