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

4, 14, 6, 622, 93, 1211, 69, 15746, 1273, 844147, 21, 3786374, 1357511, 37008721, 20028781, 201010021, 91186105, 6969801571, 224163661, 518479039339, 15633784177, 8191197319811, 83460915203, 669094978066, 691286884697

Offset: 1

Author

Zak Seidov, Silvester Resnik and Robert G. Wilson v, May 12 2018

Keywords

• more
• nonn

Comments

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}, ...

Examples

			a(1) = 4 since it is the first occurrence of a semiprime that is not part of a run of two or more semiprimes;
a(2) = 14 since it is the first of a run of exactly two consecutive semiprimes of alternating parity;
a(3) = 6 since 6 is the first of a run of exactly three consecutive semiprimes of alternating parity; etc.
		

Crossrefs

Cf. A001358, A304456, A304457.

Programs

Mathematica

Table[ SelectFirst[ Split[ Select[ Range@ 10000000, PrimeOmega@# == 2 &], Mod[#1, 2] != Mod[#2, 2] &], Length@# == n &][[1]], {n, 13}]