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A133478 a(n) = smallest semiprime s such that s + n is the next semiprime and there is no prime between s and s + n.

%I A133478 #27 Mar 18 2018 11:26:38
%S A133478 9,49,62,403,341,843,6722,3473,2869,14059,18467,26603,166126,41779,
%T A133478 74491,192061,463161,226489,344119,517421,943606,2171131,4577519,
%U A133478 584213,2560177,4356633,8367139,11174753,13191293,7319797,27841051,10644122,13683034,29492893,47735342,26837363,63305661,90455097,189662206,120175651
%N A133478 a(n) = smallest semiprime s such that s + n is the next semiprime and there is no prime between s and s + n.
%H A133478 Robert G. Wilson v, <a href="/A133478/b133478.txt">Table of n, a(n) for n = 1..60</a>.
%e A133478 a(1)=9 because there is no prime between 9 and 10.
%e A133478 a(2)=49 because there is no prime between 49 and 51.
%e A133478 a(3)=62 because there is no prime between 62 and 65.
%t A133478 nn = 20; sp1 = 4; t = Table[0, {nn}]; found = 0; fQ[s_] := Union@ PrimeQ[s] == {False}; NextSemiPrime[n_, k_: 1] := Block[{c = 0, sgn = Sign[k]}, sp = n + sgn; While[c < Abs[k], While[ PrimeOmega[sp] != 2, If[sgn < 0, sp--, sp++]]; If[ sgn < 0, sp--, sp++]; c++]; sp + If[sgn < 0, 1, -1]]; While[found < nn, sp2 = NextSemiPrime[sp1]; d = sp2 - sp1; If[d <= nn && t[[d]] == 0 && fQ[Range[sp1, sp2]], t[[d]] = sp1; found++; Print[{d, sp1}]]; sp1 = sp2]; t (* _Robert G. Wilson v_, Jun 13 2013 *)
%K A133478 nonn
%O A133478 1,1
%A A133478 _Jack Brennen_ and _Zak Seidov_, Dec 23 2007
%E A133478 a(37)-a(40) from _Jacques Tramu_, Dec 23 2007