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A215231
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Increasing gaps between semiprimes.
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6
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2, 3, 4, 6, 7, 11, 14, 19, 20, 24, 25, 28, 30, 32, 38, 47, 54, 55, 70, 74, 76, 82, 85, 87, 88, 95, 98, 107, 110, 112, 120, 123, 126, 146, 163, 166, 171, 174
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OFFSET
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1,1
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COMMENTS
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See A215232 and A217851 for the semiprimes that begin and end the gaps.
How long can these gaps be? In the Cramér model, with x = A215232(n), they are of length log(x)^2/log(log(x))(1 + o(1)) with probability 1. - Charles R Greathouse IV, Sep 07 2012
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LINKS
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EXAMPLE
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4 is here because the difference between 10 and 14 is 4, and there is no smaller semiprimes with this property.
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MATHEMATICA
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SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; nextSemiprime[n_] := Module[{m = n + 1}, While[! SemiPrimeQ[m], m++]; m]; t = {{0, 0}}; s1 = nextSemiprime[1]; While[s1 < 10^7, s2 = nextSemiprime[s1]; d = s2 - s1; If[d > t[[-1, 1]], AppendTo[t, {d, s1}]; Print[{d, s1}]]; s1 = s2]; t = Rest[t]; Transpose[t][[1]]
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PROG
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(Haskell)
a215231 n = a215231_list !! (n-1)
(a215231_list, a085809_list) = unzip $ (2, 1) : f 1 2 a065516_list where
f i v (q:qs) | q > v = (q, i) : f (i + 1) q qs
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CROSSREFS
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Cf. A005250 (increasing gaps between primes).
Cf. A239673 (increasing gaps between sphenic numbers).
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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