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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A299382 Numbers k such that k * 19^k - 1 is prime.

Original entry on oeis.org

12, 410, 33890, 91850, 146478, 189620, 280524
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 08 2018

Keywords

Comments

a(8) > 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), this sequence (b=19), A299383 (b=20).

Programs

  • Magma
    [n: n in [1..10000] |IsPrime(n*19^n-1)];
  • Mathematica
    Select[Range[1, 10000], PrimeQ[n*19^n-1] &]
  • PARI
    for(n=1, 10000, if(isprime(n*19^n-1), print1(n", ")))
    

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", ")))
    

A242338 Numbers k such that k*7^k-1 is semiprime.

Original entry on oeis.org

1, 5, 12, 21, 42, 50, 60, 242, 272
Offset: 1

Views

Author

Vincenzo Librandi, May 12 2014

Keywords

Comments

The semiprimes of this form are: 6, 84034, 166095446411, 11729463145748964146, 13102886255950779594655873516522994057, ...
From Robert Israel, Aug 19 2014: (Start)
If k is odd, k is in the sequence iff (k*7^k-1)/2 is prime.
If k == 1 (mod 3), k is in the sequence iff (k*7^k-1)/3 is prime.
a(10) >= 506. 506*7^506 - 1 is a 431-digit composite which apparently has not been factored.
(End)

Crossrefs

Cf. similar sequences listed in A242273.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [2..80] | IsSemiprime(s) where s is n*7^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(n -> `if`(n::odd, isprime((n*7^n-1)/2),
                  issemiprime(n*7^n-1)), [$1..100]); # Robert Israel, Aug 19 2014
  • Mathematica
    Select[Range[80], PrimeOmega[# 7^# - 1]==2&]
  • PARI
    for(n=1,100,if(bigomega(n*7^n-1)==2,print1(n,", "))) \\ Derek Orr, Aug 20 2014

Extensions

a(1) = 1 prepended and comment amended by Harvey P. Dale, Aug 12 2014
a(8) and a(9) from Robert Israel, Aug 20 2014
Previous Showing 11-13 of 13 results.