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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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

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).

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

A216376 Semiprimes of the form n*10^n + 1.

Original entry on oeis.org

201, 500001, 130000000000001, 280000000000000000000000000001, 340000000000000000000000000000000001, 36000000000000000000000000000000000001, 39000000000000000000000000000000000000001
Offset: 1

Author

Jonathan Vos Post, Sep 06 2012

Keywords

Comments

This is to A216347 as semiprimes A001358 are to primes A000040. The corresponding n are 2, 5, 13, 28, 34, 36, 39, ... (A216378).
a(14) >= 414*10^414 + 1. - Hugo Pfoertner, Jul 28 2019

Examples

			a(1) = 2 * 10^2 + 1 = 201 = 3 * 67.
a(2) = 5 * 10^5 + 1 = 500001 = 3 * 166667.
a(3) = 13*10^13 + 1 = 130000000000001 = 6529 * 19911165569.
a(4) = 28 * 10^28 + 1 = 29 * 9655172413793103448275862069.
		

Crossrefs

Programs

  • Magma
    IsSemiprime:= func; [s: n in [1..40] | IsSemiprime(s) where s is n*10^n + 1]; // Vincenzo Librandi, Sep 22 2012
  • Mathematica
    SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Table[n*10^n + 1, {n, 50}], SemiPrimeQ[#] &] (* T. D. Noe, Sep 07 2012 *)
    Select[Table[n*10^n + 1, {n, 50}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)

Formula

semiprimes in A064748.
Showing 1-2 of 2 results.