A114414 - OEIS

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A114414

Records in 4-almost prime gaps ordered by merit.

8, 12, 14, 21, 28 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`Next term (if it exists) associated with A014613 > 1030000. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 13 2007`
	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 (mathar(AT)strw.leidenuniv.nl), Mar 13 2007`
	CROSSREFS	`Cf. A014613, A065516, A111870, A111871, A114403-A114411, A114412-A114422.` `Sequence in context: A106669 A108979 A107071 * A032455 A050275 A033949` `Adjacent sequences: A114411 A114412 A114413 * A114415 A114416 A114417`
	KEYWORD	`nonn,more`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 25 2005`

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Last modified February 14 23:53 EST 2012. Contains 205689 sequences.