A114415 - OEIS

This site is supported by donations to The OEIS Foundation.

A114415

Records in 5-almost prime gaps ordered by merit.

16, 24, 28, 42, 56, 70 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`Next term, if it exists, is associated with indices above 100000 in A114405 and A014614. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 10 2007`
	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 (mathar(AT)strw.leidenuniv.nl), May 10 2007
	CROSSREFS	`Cf. A014614, A065516, A111870, A111871, A114403-A114411, A114412-A114422.` `Sequence in context: A052058 A105732 A166319 * A033987 A140349 A088493` `Adjacent sequences: A114412 A114413 A114414 * A114416 A114417 A114418`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 25 2005`
	EXTENSIONS	`a(6) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 10 2007`

Content is available under The OEIS End-User License Agreement .

Last modified February 15 23:53 EST 2012. Contains 205860 sequences.