%I #19 Sep 25 2022 17:17:43
%S 8203,9703,18163,35823,72687,72847,75759,95695,97959,132879,177159,
%T 194127,198763,201099,210379,223807,226887,228043,299227,306283,
%U 344779,347527,351399,360763,403467,407107,454143,487927,506467,514927,516487,532803,537367,538903,546847,556707,562819
%N Semiprimes followed by successive gaps 4, 6, 9.
%C 4, 6, 9 are the first 3 semiprimes (A001358).
%C Are there semiprimes followed by gaps {4, 6, 9, 10} = the first 4 semiprimes?
%C Answer: No, one of them would be divisible by 4.  _Giovanni Resta_, Oct 23 2018
%C Semiprimes s such that the first semiprime after s equals s+4, the next one equals s+10, and the next one equals s+19.  _Harvey P. Dale_, Sep 25 2022
%H Harvey P. Dale, <a href="/A320285/b320285.txt">Table of n, a(n) for n = 1..4000</a>
%t spQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Range[10^6/2] 2 + 1, AllTrue[# + {0, 4, 10, 19}, spQ] && Count[ Range[ #+1, #+18], x_ /; spQ@ x] == 2 &] (* _Giovanni Resta_, Oct 23 2018 *)
%t SequencePosition[If[PrimeOmega[#]==2,1,0]&/@Range[600000],{1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1}][[All,1]] (* _Harvey P. Dale_, Sep 25 2022 *)
%o (PARI) next_semiprime(n) = for(x=n, oo, if(bigomega(x)==2, return(x)))
%o is(n) = if(bigomega(n)!=2, return(0)); my(v=[n, next_semiprime(n+1), next_semiprime(next_semiprime(n+1)+1), next_semiprime(next_semiprime(next_semiprime(n+1)+1)+1)]); v[2]v[1]==4 && v[3]v[2]==6 && v[4]v[3]==9 \\ _Felix FrÃ¶hlich_, Oct 23 2018
%Y Cf. A001358.
%K nonn
%O 1,1
%A _Zak Seidov_, Oct 09 2018
