OFFSET
1,1
COMMENTS
4, 6, 9 are the first 3 semiprimes (A001358).
Are there semiprimes followed by gaps {4, 6, 9, 10} = the first 4 semiprimes?
Answer: No, one of them would be divisible by 4. - Giovanni Resta, Oct 23 2018
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
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..4000
MATHEMATICA
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 *)
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 *)
PROG
(PARI) next_semiprime(n) = for(x=n, oo, if(bigomega(x)==2, return(x)))
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 Fröhlich, Oct 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 09 2018
STATUS
approved