A352132 Numbers k such that k, k+4, 3*k+4 and 3*k+8 are all semiprimes.

6, 10, 118, 119, 129, 155, 287, 295, 299, 319, 377, 413, 447, 469, 511, 538, 629, 681, 699, 717, 785, 831, 865, 913, 1003, 1073, 1077, 1111, 1115, 1137, 1141, 1145, 1267, 1343, 1345, 1379, 1393, 1437, 1469, 1509, 1687, 1817, 1835, 1919, 1923, 1981, 2167, 2173, 2177, 2195, 2245, 2429, 2479, 2569

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 05 2022

Keywords

• nonn

Comments

Numbers k such that k and 3*k+4 are both in A175648.

Even terms are 2*k for k in A174920.

Examples

			a(4) = 119 is a term because 119 = 7*17, 119+4 = 123 = 3*41, 3*119+4 = 361 = 19^2 and 3*119+8 = 365 = 5*73 are semiprimes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A174920, A175648.

Programs

Maple

filter:= proc(x)
numtheory:-bigomega(x) = 2 and numtheory:-bigomega(x+4) = 2 and numtheory:-bigomega(3*x+4) = 2 and numtheory:-bigomega(3*x+8)=2
end proc:
select(filter, [$1..3000]);

Mathematica

okQ[k_] := AllTrue[{k, k+4, 3k+4, 3k+8}, PrimeOmega[#] == 2&];
Select[Range[3000], okQ] (* Jean-François Alcover, May 16 2023 *)