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 1-6 of 6 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 &]

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 &]

A242332 Numbers k such that k^2 + 4 is a semiprime.

Original entry on oeis.org

0, 9, 19, 21, 23, 25, 31, 41, 43, 51, 53, 55, 63, 69, 71, 75, 77, 79, 83, 91, 93, 105, 107, 109, 113, 119, 123, 129, 131, 133, 143, 145, 149, 151, 153, 157, 165, 171, 173, 175, 181, 185, 187, 191, 195, 197, 201, 209, 221, 223, 225, 227, 241, 249, 251, 257, 259
Offset: 1

Views

Author

Vincenzo Librandi, May 14 2014

Keywords

Comments

The semiprimes of this form are: 4, 85, 365, 445, 533, 629, 965, 1685, 1853, 2605, 2813, 3029, 3973, 4765, 5045, 5629, 5933, 6245, ...

Links

Crossrefs

Cf. A005473, A007591, A085722, A242330, A242331, A242333.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [0..300] | IsSemiprime(s) where s is n^2+4];
  • Mathematica
    Select[Range[0, 300], PrimeOmega[#^2 + 4] == 2 &]

A360739 Semiprimes of the form k^2 + 2.

Original entry on oeis.org

6, 38, 51, 123, 146, 291, 326, 731, 843, 1227, 1371, 1766, 1851, 2306, 2603, 2811, 2918, 3027, 3602, 4227, 4358, 4763, 5186, 5331, 5627, 6243, 6891, 7058, 7571, 8102, 8651, 9411, 13227, 14163, 15627, 17426, 17691, 18227, 18771, 19883, 20738, 22502, 23411, 24027
Offset: 1

Views

Author

Elmo R. Oliveira, Feb 18 2023

Keywords

Comments

A242330 gives the corresponding values of k.

Examples

			123 is a term because 11^2 + 2 = 123 = 3*41.

Crossrefs

Cf. A001358, A059100, A085722, A144255, A242330.

Programs

  • Mathematica
    Select[Range[0, 200]^2 + 2, PrimeOmega[#] == 2 &] (* Amiram Eldar, Feb 18 2023 *)

Formula

a(n) = A242330(n)^2 + 2.

A360740 Semiprimes of the form k^2 + 3.

Original entry on oeis.org

4, 39, 259, 327, 403, 579, 679, 1027, 1159, 1299, 1603, 1939, 2119, 2307, 3139, 3603, 4359, 4627, 6087, 6403, 7747, 9607, 10003, 10407, 10819, 11667, 13459, 13927, 14403, 16387, 18499, 21907, 23107, 26899, 28903, 30279, 30979, 33127, 35347, 36103, 36867, 38419
Offset: 1

Views

Author

Elmo R. Oliveira, Feb 18 2023

Keywords

Comments

A242331 gives the corresponding values of k.

Examples

			259 is a term because 16^2 + 3 = 259 = 7*37.

Crossrefs

Cf. A001358, A085722, A117950, A144255, A242330, A242331.

Programs

  • Mathematica
    Select[Range[0, 200]^2 + 3, PrimeOmega[#] == 2 &] (* Amiram Eldar, Feb 18 2023 *)

Formula

a(n) = A242331(n)^2 + 3.

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 1-6 of 6 results.

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