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.

User: Silvester Resnik

Silvester Resnik's wiki page.

Silvester Resnik has authored 5 sequences.

A303585 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..8.

Original entry on oeis.org

50238568800, 5824121940000, 46919196354240, 50564131254000, 80493123110400, 195778384956000, 307148642236800, 799863695270640
Offset: 1

Author

Silvester Resnik, May 25 2018

Keywords

Programs

  • PARI
    fibomod(n, m) = lift(Mod([0, 1; 1, 1], m)^(n+1))[1, 1];
    isok(n) = prod(k=0, 8, fibomod(n, n+k)==0);

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

Original entry on oeis.org

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

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

Examples

			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.
		

Crossrefs

Programs

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

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

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

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}]

A300555 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..7.

Original entry on oeis.org

175472640, 44915270400, 50238568800, 439287521400, 572836904640, 589596638400, 735284012400, 778042465200, 987189789600, 1261551677400, 1297640010240, 1307130728400, 1569978804240, 1979830125000, 2705598768600
Offset: 1

Author

Silvester Resnik, May 19 2018

Keywords

Crossrefs

Programs

  • PARI
    fibomod(n, m) = lift(Mod([0, 1; 1, 1], m)^(n+1))[1, 1];
    isok(n) = prod(k=0, 7, fibomod(n, n+k)==0);