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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A299383 Numbers k such that k * 20^k - 1 is prime.

Original entry on oeis.org

1, 18, 44, 60, 80, 123, 429, 1166, 2065, 8774, 35340, 42968, 50312, 210129
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 08 2018

Keywords

Comments

a(15) > 400000.

Crossrefs

Numbers n such that n * b^n - 1 is prime: A008864 (b=1), A002234 (b=2), A006553 (b=3), A086661 (b=4), A059676 (b=5), A059675 (b=6), A242200 (b=7), A242201 (b=8), A242202 (b=9), A059671 (b=10), A299374 (b=11), A299375 (b=12), A299376 (b=13), A299377 (b=14), A299378 (b=15), A299379 (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), this sequence (b=20).

Programs

  • Magma
    [n: n in [1..10000] |IsPrime(n*20^n-1)];
  • Mathematica
    Select[Range[1, 10000], PrimeQ[n*20^n-1] &]
  • PARI
    for(n=1, 10000, if(isprime(n*20^n-1), print1(n", ")))
    

A242341 Numbers k such that k*10^k - 1 is a semiprime.

Original entry on oeis.org

1, 6, 20, 29, 35, 40, 79, 164, 185, 198, 201, 218, 248, 249, 251, 264, 267, 274, 305, 323, 339, 344, 350, 362, 432, 539
Offset: 1

Views

Author

Vincenzo Librandi, May 12 2014

Keywords

Comments

The semiprimes of this form are: 9, 5999999, 1999999999999999999999, 2899999999999999999999999999999, ...
From Robert Israel, Sep 04 2016: (Start)
k == 1 (mod 3) is in the sequence iff (k*10^k-1)/3 is prime.
The sequence includes 185, 198, 201, 251, 267, 274, and 1795. (End)
a(27) >= 596. Below 1000, 785 and 833 are in the sequence. Unknown factorization for 596, 669, 917, 933. - Hugo Pfoertner, Jul 29 2019

Crossrefs

Cf. similar sequences listed in A242273.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [2..70] | IsSemiprime(s) where s is n*10^n-1];
    
  • Maple
    issemiprime:= proc(n) local F, t;
        F:= ifactors(n, easy)[2];
        t:= add(f[2], f=F);
        if t = 1 then
           if type(F[1][1], integer) then return false fi
        elif t = 2 then
           return not hastype(F, name)
        else # t > 2
           return false
        fi;
        F:= ifactors(n)[2];
        return evalb(add(f[2], f=F)=2);
    end proc:
    select(t -> issemiprime(t*10^t-1), [$1..80]); # Robert Israel, Sep 04 2016
  • Mathematica
    Select[Range[70], PrimeOmega[# 10^# - 1]==2&]
  • PARI
    is(n)=bigomega(n*10^n-1)==2 \\ Charles R Greathouse IV, Sep 04 2016

Extensions

Terms 1 and 79 from Robert Israel, Sep 04 2016
a(8)-a(26) from Hugo Pfoertner, Jul 29 2019

A216346 Primes of the form n*10^n - 1.

Original entry on oeis.org

199, 2999, 799999999, 1099999999999, 14999999999999999, 38999999999999999999999999999999999999999, 59999999999999999999999999999999999999999999999999999999999999, 71999999999999999999999999999999999999999999999999999999999999999999999999
Offset: 1

Author

Michel Lagneau, Sep 04 2012

Keywords

Comments

The corresponding n are in A059671.
a(9) = 769999999….999999 contains 79 digits.
a(10) = 1169999999….999999 contains 120 digits.

Crossrefs

Cf. A059671.

Programs

  • Mathematica
    lst={}; Do[ p=n*10^n- 1; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 60}]; lst
    Select[Table[n*10^n-1,{n,100}],PrimeQ] (* Harvey P. Dale, Sep 17 2023 *)
Previous Showing 11-13 of 13 results.