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 1-6 of 6 results.

A098980 Duplicate of A007647.

Original entry on oeis.org

1, 3, 9, 21, 363, 2161, 4839, 49521, 105994
Offset: 1

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Author

Keywords

A242176 Numbers k such that k*6^k + 1 is prime.

Original entry on oeis.org

1, 2, 91, 185, 387, 488, 747, 800, 9901, 10115, 12043, 13118, 30981, 51496
Offset: 1

Views

Author

Vincenzo Librandi, May 08 2014

Keywords

Crossrefs

Cf. numbers n such that n*k^n + 1 is prime: A005849 (k=2), A006552 (k=3), A007646 (k=4), this sequence (k=6), A242177 (k=7), A242178 (k=8), A007647 (k=10), A242196 (k=12), A242197 (k=14), A242198 (k=15), A242199 (k=16), A007648 (k=18).

Programs

  • Magma
    [n: n in [0..1500] | IsPrime(n*6^n+1)];
    
  • Mathematica
    Select[Range[1500], PrimeQ[# 6^# + 1] &]
  • PARI
    is(n)=ispseudoprime(n*6^n+1) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(9)-a(14) from Loeh's list (see Links) - Bruno Berselli, May 08 2014

A216347 Primes of the form n*10^n + 1.

Original entry on oeis.org

11, 3001, 9000000001, 21000000000000000000001
Offset: 1

Views

Author

Michel Lagneau, Sep 04 2012

Keywords

Comments

The corresponding n are in A007647.
a(5) = 363000000….00001 contains 366 digits.

Crossrefs

Cf. A007647.

Programs

  • Mathematica
    lst={}; Do[ p=n*10^n+ 1; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 21}]; lst
    Select[Table[n*10^n+1,{n,40}],PrimeQ] (* Harvey P. Dale, Jul 18 2020 *)

A216378 Numbers m such that m*10^m + 1 is a semiprime.

Original entry on oeis.org

2, 5, 13, 28, 34, 36, 39, 111, 117, 123, 181, 184, 187
Offset: 1

Views

Author

Jonathan Vos Post, Sep 06 2012

Keywords

Comments

This is to A007647 as semiprimes A001358 is to primes A000040. The corresponding semiprimes are A216376 = {201, 500001, 130000000000001, 280000000000000000000000000001, ...}.
a(14) >= 414. - Daniel Suteu, Jul 09 2019

Examples

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

Crossrefs

Cf. similar sequences listed in A242203.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..70] | IsSemiprime(s) where s is n*10^n+1]; // Vincenzo Librandi, May 10 2014
  • Mathematica
    Select[Range[40], PrimeOmega[# 10^# + 1] == 2 &] (* Alonso del Arte, Sep 08 2012 *)

Extensions

a(8)-a(13) from Daniel Suteu, Jul 09 2019

A265013 Numbers n such that n*9^n + 1 is prime.

Original entry on oeis.org

2, 12382, 27608, 31330, 117852
Offset: 1

Author

Tim Johannes Ohrtmann, Nov 30 2015

Keywords

Comments

All terms are even. - Robert Israel, Jan 18 2016

Programs

  • Magma
    [n: n in [0..100000] | IsPrime(n*9^n+1)];
  • Mathematica
    Select[Range[100000], PrimeQ[# 9^# + 1] &]
  • PARI
    for(n=1,100000, if(isprime(n*9^n+1), print1(n,", ")))
    

A338412 Numbers k such that k * 20^k + 1 is prime.

Original entry on oeis.org

3, 6207, 8076, 22356, 151456
Offset: 1

Author

Tim Johannes Ohrtmann, Oct 25 2020

Keywords

Comments

a(6) > 219976.

Crossrefs

Numbers k such that k * b^k + 1 is prime: A006093 (b=1), A005849 (b=2), A006552 (b=3), A007646 (b=4), A242176 (b=6), A242177 (b=7), A242178 (b=8), A265013 (b=9), A007647(b=10), A242196(b=12), A242197 (b=14), A242198 (b=15), A242199 (b=16), A007648 (b=18), 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, ", ")))
    
Showing 1-6 of 6 results.