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Even semiprimes such that the next semiprime is also even.
1

%I #13 Aug 01 2020 18:27:53

%S 4,10,58,274,382,454,458,538,614,1082,1234,1318,1478,1618,1718,1874,

%T 2062,2374,2554,2846,2902,3574,3722,3998,4174,4258,4474,4946,5098,

%U 5414,5422,5498,6334,6598,6658,6686,6718,6778,6914,6922,7054,7346,7534,7642,7702,7754,7838,8038,8098,8422,8434,8674,8818

%N Even semiprimes such that the next semiprime is also even.

%H Robert Israel, <a href="/A328036/b328036.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3)=58 is a member because 58=2*29 is an even semiprime and the next semiprime is 62, which is also even.

%p sp:= select(t -> numtheory:-bigomega(t)=2, [$1..20000]):

%p sp[select(t -> sp[t]::even and sp[t+1]::even, [$1..nops(sp)-1])];

%t Select[Partition[Select[Range[10000],PrimeOmega[#]==2&],2,1],AllTrue[#,EvenQ]&][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 01 2020 *)

%Y Cf. A001358. Includes 2*A069142.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Oct 02 2019