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

1,1

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A136196.

Sequence in context: A248628 A217608 A264779 * A305349 A030465 A147270

Adjacent sequences: A133606 A133607 A133608 * A133610 A133611 A133612

Keyword

nonn

Author

Zak Seidov, Dec 28 2007

Status

approved