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Least semiprime of a run of exactly n even semiprimes.
2

%I #20 Jun 03 2018 11:57:10

%S 22,4,454,300746,111614,14491726,1096669582,42205941082,85933755478,

%T 746001905114,39682041123518

%N Least semiprime of a run of exactly n even semiprimes.

%C Runs of semiprimes of the same parity: {4, 6}, {9}, {10, 14}, {15, 21}, {22}, {25}, {26}, {33}, {34}, {35}, {38}, {39}, {46}, {49, 51, 55, 57}, {58, 62}, {65, 69}, {74}, {77}, {82}, {85}, {86}, {87, 91, 93}, {94}, ...

%C a(12) > 2*10^14.

%e a(1) = 22 since it is the first occurrence of a single even semiprime;

%e a(2) = 4 since 4 is the first of two consecutive even semiprimes in the sequence of semiprimes;

%e a(3) = 454 since it is the first of three consecutive even semiprimes in the sequence of semiprimes; etc.

%t SplitBy[ Select[ Range@ 100, PrimeOmega@# == 2 &], Mod[#, 2] &] (* to view the runs of semiprimes of the same parity *)

%Y Cf. A001358, A304457, A304458.

%K nonn,more

%O 1,1

%A _Zak Seidov_, _Silvester Resnik_ and _Robert G. Wilson v_, May 12 2018