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A114403
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3-almost prime gaps. First differences of A014612.
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23
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4, 6, 2, 7, 1, 2, 12, 2, 1, 5, 2, 11, 3, 2, 2, 5, 1, 2, 14, 6, 1, 3, 3, 5, 4, 2, 1, 7, 1, 5, 8, 9, 1, 5, 1, 10, 1, 5, 1, 1, 2, 1, 7, 4, 2, 2, 5, 12, 5, 10, 8, 1, 5, 2, 4, 2, 1, 1, 9, 3, 3, 5, 2, 5, 2, 4, 3, 2, 1, 1, 4, 2, 18, 6, 2, 4, 3, 7, 1, 5, 5, 2, 9, 2, 1, 6, 3, 3, 1, 4, 11, 2, 1, 11, 3, 2, 2, 4, 2, 6, 5, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
| a(n) = A014612(n+1) - A014612(n).
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EXAMPLE
| a(1) = 4 = 12-8 where 8 is the first 3-almost prime and 12 is the second.
a(2) = 6 = 18-12
a(3) = 2 = 20-18
a(4) = 7 = 27-20
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MAPLE
| is3Alm := proc(n::integer) local ifa, ex, i ; ifa := op(2, ifactors(n)) ; ex := 0 ; for i from 1 to nops(ifa) do ex := ex+ op(2, op(i, ifa)) ; od : if ex = 3 then RETURN(true) ; else RETURN(false) ; fi ; end: A014612 := proc(n::integer) local resul, i; i :=1; resul := 8 ; while i < n do resul := resul + 1 ; if is3Alm(resul) then i := i+1 ; fi ; od ; RETURN(resul) ; end: A114403 := proc(n::integer) RETURN(A014612(n+1)-A014612(n)) ; end: for n from 1 to 160 do printf("%d, ", A114403(n)) ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 25 2006
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CROSSREFS
| Cf. A014612, A065516, A111870, A111871, A114403-A114411, A114412-A114422.
Sequence in context: A010669 A029677 A045867 * A137662 A153124 A066252
Adjacent sequences: A114400 A114401 A114402 * A114404 A114405 A114406
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 25 2005
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EXTENSIONS
| Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 25 2006
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