A304456 -id:A304456 - cp's OEIS frontend

A304457 Least semiprime of a run of exactly n odd semiprimes.

9, 15, 87, 49, 235, 403, 1241, 1383, 1047, 3341, 4359, 9663, 11499, 14163, 5947, 11183, 19103, 45151, 50943, 31367, 173747, 306003, 215021, 191303, 86663, 62797, 362609, 425405, 346727, 531247, 676067, 721311, 793469, 741899, 1637447, 2896177, 311843, 4477649, 7702927, 1208153

Offset: 1

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

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}, ....

a(108) = 85305236689; a(101-107), if any, should be > 116820000000. - Zak Seidov, Aug 26 2021

			a(1) = 9 since it is the first occurrence of a single odd semiprime;
a(2) = 15 since 15 is the first of two consecutive odd semiprimes in the sequence of semiprimes;
a(3) = 87 since 87 is the first of exactly three consecutive odd semiprimes;
a(4) = 49 since 49 is the first of exactly four consecutive odd semiprimes; etc.

Silvester Resnik, Table of n, a(n) for n = 1..100

Cf. A001358, A304456, A304458.

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

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

Original entry on oeis.org

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

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

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}, ...

			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.

Cf. A001358, A304456, A304457.

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

cp's OEIS Frontend

A304457 Least semiprime of a run of exactly n odd semiprimes.

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