A092125 Numbers n such that n, n+2, n+4 are semiprimes.

91, 119, 141, 183, 201, 213, 215, 217, 287, 299, 301, 319, 391, 411, 413, 469, 515, 533, 579, 667, 685, 695, 789, 813, 1055, 1077, 1133, 1135, 1137, 1145, 1165, 1203, 1253, 1313, 1343, 1345, 1347, 1383, 1385, 1387, 1389, 1401, 1561, 1639, 1685, 1687, 1761

Offset: 1

Author

Zak Seidov, Feb 22 2004

Keywords

• easy
• nonn

Comments

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

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

Mathematica

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 *)
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 *)