OFFSET
1,1
COMMENTS
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
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
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