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A352132
Numbers k such that k, k+4, 3*k+4 and 3*k+8 are all semiprimes.
2
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Mar 05 2022
STATUS
approved