A092125 - OEIS

%I #14 Sep 08 2022 08:45:13

%S 91,119,141,183,201,213,215,217,287,299,301,319,391,411,413,469,515,

%T 533,579,667,685,695,789,813,1055,1077,1133,1135,1137,1145,1165,1203,

%U 1253,1313,1343,1345,1347,1383,1385,1387,1389,1401,1561,1639,1685,1687,1761

%N Numbers n such that n, n+2, n+4 are semiprimes.

%C Semiprimes in arithmetic progression. All terms are odd, see also A056809.

%H Harvey P. Dale, <a href="/A092125/b092125.txt">Table of n, a(n) for n = 1..1000</a>

%t PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[Table[ #[[2]], {1}] & /@ FactorInteger[n]]; Select[ Range[ 1792], PrimeFactorExponentsAdded[ # ] == PrimeFactorExponentsAdded[ # + 2] == PrimeFactorExponentsAdded[ # + 4] == 2 &] (* _Robert G. Wilson v_, Feb 24 2004 *)

%t SequencePosition[Table[If[PrimeOmega[n]==2,1,0],{n,2000}],{1,_,1,_,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Feb 17 2020 *)

%o (Magma)IsSemiprime:=func< n| &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [2..4300]|IsSemiprime(n) and IsSemiprime(n+2) and IsSemiprime(n+4)] // _Vincenzo Librandi_, Dec 16 2010

%Y Cf. A056809, A070552, A092126, A092127, A092128, A092129.

%K easy,nonn

%O 1,1

%A _Zak Seidov_, Feb 22 2004