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A320285
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Semiprimes followed by successive gaps 4, 6, 9.
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1
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8203, 9703, 18163, 35823, 72687, 72847, 75759, 95695, 97959, 132879, 177159, 194127, 198763, 201099, 210379, 223807, 226887, 228043, 299227, 306283, 344779, 347527, 351399, 360763, 403467, 407107, 454143, 487927, 506467, 514927, 516487, 532803, 537367, 538903, 546847, 556707, 562819
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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