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 1-4 of 4 results.

A242331 Numbers k such that k^2 + 3 is a semiprime.

Original entry on oeis.org

1, 6, 16, 18, 20, 24, 26, 32, 34, 36, 40, 44, 46, 48, 56, 60, 66, 68, 78, 80, 88, 98, 100, 102, 104, 108, 116, 118, 120, 128, 136, 148, 152, 164, 170, 174, 176, 182, 188, 190, 192, 196, 200, 204, 212, 220, 226, 232, 234, 238, 246, 250, 252, 258, 260, 262, 266
Offset: 1

Views

Author

Vincenzo Librandi, May 14 2014

Keywords

Comments

The semiprimes of this form are: 4, 39, 259, 327, 403, 579, 679, 1027, 1159, 1299, 1603, 1939, 2119, 2307, 3139, 3603, 4359, 4627, ...

Links

Crossrefs

Cf. A049422, A049423, A085722, A242330, A242332, A242333.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [0..300] | IsSemiprime(s) where s is n^2+3];
  • Mathematica
    Select[Range[300], PrimeOmega[#^2 + 3] == 2 &]

A242330 Numbers k such that k^2 + 2 is a semiprime.

Original entry on oeis.org

2, 6, 7, 11, 12, 17, 18, 27, 29, 35, 37, 42, 43, 48, 51, 53, 54, 55, 60, 65, 66, 69, 72, 73, 75, 79, 83, 84, 87, 90, 93, 97, 115, 119, 125, 132, 133, 135, 137, 141, 144, 150, 153, 155, 159, 161, 165, 169, 174, 183, 186, 187, 189, 191, 192, 195, 198
Offset: 1

Views

Author

Vincenzo Librandi, May 14 2014

Keywords

Comments

The semiprimes of this form are: 6, 38, 51, 123, 146, 291, 326, 731, 843, 1227, 1371, 1766, 1851, 2306, 2603, 2811, 2918, 3027, 3602, ....
There are no four consecutive terms in this sequence, that is, a(n) > a(n-3) + 3 (check mod 6). Probably sieve theory can show that this sequence has density 0. - Charles R Greathouse IV, Feb 24 2023

Links

Crossrefs

Cf. A056899, A067201, A085722, A242331, A242332, A242333.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [2..200] | IsSemiprime(s) where s is n^2+2];
  • Mathematica
    Select[Range[300], PrimeOmega[#^2 + 2] == 2 &]
  • PARI
    issemi(n)=forprime(p=2,997,if(n%p==0, return(isprime(n/p)))); bigomega(n)==2
is(n)=issemi(n^2+2) \\ Charles R Greathouse IV, Feb 24 2023

Formula

a(n) > 2n for n > 1. - Charles R Greathouse IV, Feb 24 2023

A242333 Numbers k such that k^2 + 5 is a semiprime.

Original entry on oeis.org

1, 2, 3, 4, 8, 9, 14, 18, 21, 22, 24, 26, 27, 28, 30, 33, 42, 44, 51, 54, 57, 58, 62, 63, 64, 68, 69, 82, 84, 86, 90, 93, 98, 99, 102, 104, 108, 111, 118, 132, 134, 138, 144, 152, 154, 156, 166, 174, 177, 180, 183, 184, 186, 188, 189, 194, 208, 210, 212, 216
Offset: 1

Views

Author

Vincenzo Librandi, May 14 2014

Keywords

Comments

The semiprimes of this form are: 6, 9, 14, 21, 69, 86, 201, 329, 446, 489, 581, 681, 734, 789, 905, 1094, 1769, 1941, 2606, 2921, 3254, ...

Links

Crossrefs

Cf. A056905, A078402, A085722, A242330, A242331, A242332.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [0..300] | IsSemiprime(s) where s is n^2+5];
  • Mathematica
    Select[Range[0, 300], PrimeOmega[#^2 + 5] == 2 &]

A360741 Semiprimes of the form k^2 + 4.

Original entry on oeis.org

4, 85, 365, 445, 533, 629, 965, 1685, 1853, 2605, 2813, 3029, 3973, 4765, 5045, 5629, 5933, 6245, 6893, 8285, 8653, 11029, 11453, 11885, 12773, 14165, 15133, 16645, 17165, 17693, 20453, 21029, 22205, 22805, 23413, 24653, 27229, 29245, 29933, 30629, 32765, 34229
Offset: 1

Views

Author

Elmo R. Oliveira, Feb 18 2023

Keywords

Comments

A242332 gives the corresponding values of k.
Except for 4, all terms == 5 (mod 8). - Robert Israel, Feb 18 2023

Examples

			85 is a term because 9^2 + 4 = 85 = 5*17.

Crossrefs

Cf. A001358, A085722, A087475, A144255, A242330, A242331, A242332.

Programs

  • Maple
    select(t -> numtheory:-bigomega(t)=2, [seq(i^2+4,i=0..1000)]); # Robert Israel, Feb 18 2023
  • Mathematica
    Select[Range[0, 200]^2 + 4, PrimeOmega[#] == 2 &] (* Amiram Eldar, Feb 18 2023 *)

Formula

a(n) = A242332(n)^2 + 4.
Showing 1-4 of 4 results.

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