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A304458 Least semiprime of a run of exactly n with alternating parity.

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%I A304458 #12 May 12 2024 10:03:29
%S A304458 4,14,6,622,93,1211,69,15746,1273,844147,21,3786374,1357511,37008721,
%T A304458 20028781,201010021,91186105,6969801571,224163661,518479039339,
%U A304458 15633784177,8191197319811,83460915203,669094978066,691286884697
%N A304458 Least semiprime of a run of exactly n with alternating parity.
%C A304458 Runs of semiprimes of alternating 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, 95, 106, 111}, ...
%e A304458 a(1) = 4 since it is the first occurrence of a semiprime that is not part of a run of two or more semiprimes;
%e A304458 a(2) = 14 since it is the first of a run of exactly two consecutive semiprimes of alternating parity;
%e A304458 a(3) = 6 since 6 is the first of a run of exactly three consecutive semiprimes of alternating parity; etc.
%t A304458 Table[ SelectFirst[ Split[ Select[ Range@ 10000000, PrimeOmega@# == 2 &], Mod[#1, 2] != Mod[#2, 2] &], Length@# == n &][[1]], {n, 13}]
%Y A304458 Cf. A001358, A304456, A304457.
%K A304458 more,nonn
%O A304458 1,1
%A A304458 _Zak Seidov_, _Silvester Resnik_ and _Robert G. Wilson v_, May 12 2018