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.

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A269264 Numbers k such that (2^k-1)^2 - 2 is a semiprime.

Original entry on oeis.org

5, 9, 13, 16, 23, 24, 28, 35, 37, 38, 40, 47, 48, 51, 52, 57, 61, 65, 67, 70, 79, 83, 84, 85, 88, 90, 102, 111, 144, 148, 157, 162, 168, 169, 177, 181, 190, 237, 246, 298, 308, 346
Offset: 1

Views

Author

Vincenzo Librandi, Feb 21 2016

Keywords

Comments

a(43) >= 385. - Serge Batalov, Feb 26 2023

Examples

			a(1) = 5 because 31^2-2 = 959 = 7*137 which is semiprime.
a(2) = 9 because 511^2-2 = 261119 = 23*11353 which is semiprime.

Links

Crossrefs

Cf. A091515, A091516, A268574, A360993, A360994.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [2..120]| IsSemiprime(s) where s is (2^n-1)^2-2];
  • Mathematica
    Select[Range[120], PrimeOmega[(2^# - 1)^2 - 2] == 2 &]
  • PARI
    isok(n) = bigomega((2^n-1)^2-2) == 2; \\ Michel Marcus, Feb 22 2016

Extensions

a(29)-a(42) from Hugo Pfoertner, Aug 05 2019

A360993 Numbers k such that (2^k - 1)^3 + 2 is a semiprime.

Original entry on oeis.org

4, 5, 8, 12, 13, 18, 20, 29, 38, 56, 60, 62, 76, 82, 101, 118, 202, 210, 230, 276, 328, 332, 336, 338, 368
Offset: 1

Views

Author

Serge Batalov, Feb 27 2023

Keywords

Comments

a(26) >= 406.
438, 500, 526, 604, 648, 696 are also in this sequence, but their positions cannot be established before finding any factor for the values corresponding to the following "blockers": 406, 496, 528.
2382, 2733, 2910, 3368, 3508, 5338, 7705, 11185, 19905, 23814, 38545, 179294 are larger terms of this sequence, but their positions cannot be established. These produce "trivial" semiprimes where one prime is small (e.g., 3 or 11).

Examples

			a(1) = 4 because 15^3 + 2 = 3377 = 11 * 307, which is semiprime.
a(2) = 5 because 31^3 + 2 = 29793 = 3 * 9931, which is semiprime.

Links

Crossrefs

Cf. A091515, A091516, A100899, A100900, A268574, A269264, A360994.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [2..70]| IsSemiprime(s) where s is (2^n-1)^3+2];
  • Mathematica
    Select[Range[70], PrimeOmega[(2^# - 1)^3 - 2] == 2 &]
  • PARI
    isok(n) = bigomega((2^n-1)^3+2) == 2;

Extensions

a(20)-a(26) from Serge Batalov, Mar 03 2023
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