OFFSET
1,1
COMMENTS
Matomäki & Teräväinen prove that there is almost always (in the sense of natural density) a semiprime in (x, x + log(x)^2.1]. Under RH the exponent can be chosen as 2 + e for any e > 0. - Charles R Greathouse IV, Oct 03 2022
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..38 (terms < 10^13)
Kaisa Matomäki and Joni Teräväinen, Almost primes in almost all short intervals II, arXiv:2207.05038 [math.NT].
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][[2]]
PROG
(PARI) r=0; s=2; for(n=3, 1e7, if(bigomega(n)==2, if(n-s>r, r=n-s; print1(s", ")); s=n)) \\ Charles R Greathouse IV, Sep 07 2012
CROSSREFS
KEYWORD
nonn,hard,nice
AUTHOR
T. D. Noe, Aug 07 2012
EXTENSIONS
a(27)-a(31) from Donovan Johnson, Aug 07 2012
STATUS
approved