cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A304456 Least semiprime of a run of exactly n even semiprimes.

Original entry on oeis.org

22, 4, 454, 300746, 111614, 14491726, 1096669582, 42205941082, 85933755478, 746001905114, 39682041123518
Offset: 1

Views

Author

Keywords

Comments

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(12) > 2*10^14.

Examples

			a(1) = 22 since it is the first occurrence of a single even semiprime;
a(2) = 4 since 4 is the first of two consecutive even semiprimes in the sequence of semiprimes;
a(3) = 454 since it is the first of three consecutive even semiprimes in the sequence of semiprimes; etc.
		

Crossrefs

Programs

  • Mathematica
    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

Views

Author

Keywords

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

Programs

  • Mathematica
    Table[ SelectFirst[ Split[ Select[ Range@ 10000000, PrimeOmega@# == 2 &], Mod[#1, 2] != Mod[#2, 2] &], Length@# == n &][[1]], {n, 13}]
Showing 1-2 of 2 results.