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

1,1

Comments

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

Even terms are 2*k for k in A174920.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A001358, A174920, A175648.

Sequence in context: A117310 A174322 A359332 * A124902 A153022 A262081

Adjacent sequences: A352129 A352130 A352131 * A352133 A352134 A352135

Keyword

nonn

Author

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

Status

approved