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%I #18 Oct 03 2022 10:36:23
%S 4,6,10,15,26,95,597,1418,2681,6559,16053,17965,32777,35103,35981,
%T 340894,1069541,1589662,3586843,5835191,139139887,251306317,285074689,
%U 327023206,751411951,981270902,2655397631,5238280946,6498130361,8512915573,16328958619
%N Least semiprime m such that the next semiprime is m + A215231(n).
%C The semiprime m + A215231(n) is in A217851.
%C 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
%H Donovan Johnson, <a href="/A215232/b215232.txt">Table of n, a(n) for n = 1..38</a> (terms < 10^13)
%H Kaisa Matomäki and Joni Teräväinen, <a href="https://arxiv.org/abs/2207.05038">Almost primes in almost all short intervals II</a>, arXiv:2207.05038 [math.NT].
%t 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]]
%o (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
%Y Cf. A001358 (semiprimes), A131109, A215231, A217851.
%Y Cf. A002386 (increasing gaps between primes).
%K nonn,hard,nice
%O 1,1
%A _T. D. Noe_, Aug 07 2012
%E a(27)-a(31) from _Donovan Johnson_, Aug 07 2012
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