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A215231 Increasing gaps between semiprimes. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A215232 and A217851 for the semiprimes that begin and end the gaps.

Records in A065516. - R. J. Mathar, Aug 09 2012

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

a(n) = A065516(A085809(n)). - Reinhard Zumkeller, Mar 23 2014

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

4 is here because the difference between 10 and 14 is 4, and there is no smaller semiprimes with this property.

MATHEMATICA

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]]

PROG

(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

                | otherwise = f (i + 1) v qs

-- Reinhard Zumkeller, Mar 23 2014

CROSSREFS

Cf. A001358 (semiprimes), A131109, A215232, A217851.

Cf. A005250 (increasing gaps between primes).

Cf. A239673 (increasing gaps between sphenic numbers).

Sequence in context: A130690 A308189 A074885 * A301512 A091336 A002235

Adjacent sequences:  A215228 A215229 A215230 * A215232 A215233 A215234

KEYWORD

nonn,hard,more

AUTHOR

T. D. Noe, Aug 07 2012

EXTENSIONS

a(27)-a(31) from Donovan Johnson, Aug 07 2012

a(32)-a(38) from Donovan Johnson, Sep 20 2012

STATUS

approved

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Last modified November 28 05:30 EST 2021. Contains 349401 sequences. (Running on oeis4.)