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 1-3 of 3 results.

A242273 Numbers n such that n*2^n - 1 is a semiprime.

Original entry on oeis.org

5, 7, 8, 9, 10, 12, 18, 20, 25, 32, 37, 39, 72, 80, 85, 90, 97, 142, 150, 159, 163, 168, 169, 186, 192, 211, 231, 272, 305, 349, 363, 369, 375, 463, 465, 615, 668, 672, 789, 797, 817, 859, 908, 938, 951, 1092, 1123
Offset: 1

Views

Author

Vincenzo Librandi, May 12 2014

Keywords

Comments

The semiprimes of this form are: 159, 895, 2047, 4607, 10239, ... (A242115).
a(48) >= 1152. - Hugo Pfoertner, Jul 29 2019

Links

Crossrefs

Cf. numbers n such that n*k^n - 1 is semiprime: this sequence (k=2), A242274 (k=3), A242335 (k=4), A242336 (k=5), A242337 (k=6), A242338 (k=7), A242339 (k=8), A242340 (k=9), A242341 (k=10).
Cf. A002234, A003261, A242115, A242175.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [2..1000] | IsSemiprime(s) where s is n*2^n-1];
  • Mathematica
    Select[Range[1000], PrimeOmega[# 2^# - 1]==2&]

Formula

A003261(a(n)) = A242115(n). - Amiram Eldar, Nov 27 2019

Extensions

a(28)-a(29) from Luke March, Aug 05 2015
a(30)-a(42) from Carl Schildkraut, Aug 18 2015
Corrected and extended by Luke March, Sep 01 2015
Missing terms a(26)-a(27) inserted by Amiram Eldar, Nov 27 2019

A242203 Numbers n such that n*3^n + 1 is semiprime.

Original entry on oeis.org

1, 3, 10, 16, 20, 22, 24, 34, 39, 56, 63, 108, 128, 194, 202, 212, 214, 218, 314, 364, 662, 722
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2014

Keywords

Comments

The semiprimes of this form are 4, 82, 590491, 688747537, 69735688021, 690383311399, 6778308875545, 567024177788663347, 158049650967740074414, 29307467449532190083956645177, ...
a(23) >= 894. - Hugo Pfoertner, Aug 03 2019

Links

Crossrefs

Cf. numbers n such that n*k^n + 1 is semiprime: A242175 (k=2), this sequence (k=3), A242204 (k=4), A242205 (k=5), A242269 (k=6), A242270 (k=7), A242271 (k=8), A242272 (k=9), A216378 (k=10).
Cf. A006552, A050914.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..130] | IsSemiprime(s) where s is n*3^n+1];
  • Mathematica
    Select[Range[130], PrimeOmega[# 3^# + 1] == 2 &]
  • PARI
    isok(n) = bigomega(n*3^n + 1)==2; \\ Michel Marcus, Mar 30 2019

Extensions

a(14)-a(20) from Luke March, Jul 30 2015
a(21)-a(22) from Daniel Suteu, Mar 30 2019

A242116 Cullen semiprimes: Semiprimes of the form k*2^k + 1.

Original entry on oeis.org

9, 25, 65, 161, 2049, 4609, 22529, 1048577, 44040193, 283467841537, 1202590842881, 256065421246102339102334047485953, 4259306016766850789028922770063361, 356615920533143509709616588588493085605889, 57729314674570665269045550892293179276409335447553
Offset: 1

Views

Author

K. D. Bajpai, May 04 2014

Keywords

Comments

The k-th Cullen number Cullen(k) = k*2^k + 1.
If Cullen(k) is semiprime, it is in the sequence.
The next term, a(16), has 52 digits.

Examples

			a(4) = 161 = (5*2^5+1) is 5th Cullen number and 161 = 7 * 23 is semiprime.
a(5) = 2049 = (8*2^8+1) is 8th Cullen number and 2049 = 3 * 683 is semiprime.

Links

Crossrefs

Cf. A001358, A002064, A003261, A005849, A242175.

Programs

  • Magma
    IsSemiprime:=func; [s: n in [1..200] | IsSemiprime(s) where s is n*2^n+1]; // // Vincenzo Librandi, May 07 2014
  • Maple
    with(numtheory): A242116:= proc(); if bigomega(x*2^x+1) = 2 then RETURN (x*2^x+1);  fi; end: seq(A242116 (), x=1..200);
  • Mathematica
    cullen[n_] := n * 2^n + 1; Select[cullen[Range[35]], PrimeOmega[#] == 2 &] (* Amiram Eldar, Nov 27 2019 *)
  • PARI
    select(n->bigomega(n)==2, vector(90,n,n<Charles R Greathouse IV, May 06 2014

Formula

a(n) = A002064(A242175(n)). - Amiram Eldar, Nov 27 2019
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.