A133609 Numbers k such that k, k+2 and k+4 are consecutive semiprimes.

183, 287, 319, 411, 413, 469, 515, 533, 579, 667, 685, 789, 813, 1055, 1077, 1133, 1145, 1165, 1203, 1253, 1313, 1347, 1383, 1385, 1387, 1389, 1561, 1685, 1687, 1793, 1795, 1817, 1839, 1849, 1919, 1937, 1957, 1959, 2045, 2047, 2155, 2227, 2315, 2317

Offset: 1

Author

Zak Seidov, Dec 28 2007

Keywords

• nonn

Comments

Terms k in A136196 such that k+2 are also in A136196.

All terms are odd, so it is a subsequence of A161945. - Michel Marcus, Oct 15 2013

Examples

			183, 185 and 187 are 59th, 60th and 61st semiprimes,
287, 289 and 291 are 89th, 90th and 91st semiprimes,
319, 321 and 323 are 101st, 102nd and 103rd semiprimes.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A136196.

Programs

Mathematica

Select[Range[2317],AllTrue[{#,#+2,#+4},PrimeOmega[#]==2&]&&AllTrue[{#+1,#+3},PrimeOmega[#]!=2&]&] (* James C. McMahon, Mar 29 2025 *)

PARI

isok(n) = (bigomega(n) == 2) && (bigomega(n+1) != 2) && (bigomega(n+2) == 2) && (bigomega(n+3) != 2) && (bigomega(n+4) == 2); \\ Michel Marcus, Oct 15 2013