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 1-8 of 8 results.

A252656 Numbers n such that 3^n - n is a semiprime.

Original entry on oeis.org

4, 6, 10, 25, 28, 32, 98, 124, 146, 164, 182, 190, 200, 220, 226, 230, 248, 280, 362, 376, 418, 446, 518, 544
Offset: 1

Views

Author

Vincenzo Librandi, Dec 20 2014

Keywords

Comments

Are there odd members of the sequence other than 25? There are no others < 10000. An odd number m is in the sequence iff (3^m - m)/2 is prime. - Robert Israel, Jan 02 2015
No more odd terms after a(4) = 25 for m < 200000. a(25) >= 626. - Hugo Pfoertner, Aug 07 2019

Examples

			4 is in this sequence because 3^4 - 4 = 7*11 is semiprime.
10 is in this sequence because 3^10 - 10 = 43*1373 and these two factors are prime.

Links

Crossrefs

Cf. numbers m such that k^m - m is a semiprime: A165767 (k = 2), this sequence (k = 3), A252657 (k = 4), A252658 (k = 5), A252659 (k = 6), A252660 (k = 7), A252661 (k = 8), A252662 (k = 9), A252663 (k = 10).
Cf. A001358 (semiprimes), A058037, A252788.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [2..150] | IsSemiprime(s) where s is 3^m-m];
  • Maple
    select(n -> numtheory:-bigomega(3^n - n) = 2, [$1..150]); # Robert Israel, Jan 02 2015
  • Mathematica
    Select[Range[150], PrimeOmega[3^# - #] == 2 &]
  • PARI
    is(m) = bigomega(3^m-m)==2 \\ Felix Fröhlich, Dec 30 2014
  • PARI
    n=1;while(n<100,s=3^n-n;c=0;forprime(p=1,10^4,if(s%p,c++);if(s%p==0,s1=s/p;if(ispseudoprime(s1),print1(n,", ");c=0;break);if(!ispseudoprime(s1),c=0;break)));if(!c,n++);if(c,if(bigomega(s)==2,print1(n,", "));n++)) \\ Derek Orr, Jan 02 2015

Extensions

a(10) from Felix Fröhlich, Dec 30 2014
a(11)-a(14) from Charles R Greathouse IV, Jan 02 2015
a(15)-a(24) from Luke March, Aug 21 2015

A252789 Numbers m such that 4^m + m is a semiprime.

Original entry on oeis.org

7, 19, 39, 43, 87, 135, 147, 177, 223, 255, 403
Offset: 1

Views

Author

Vincenzo Librandi, Dec 24 2014

Keywords

Comments

From Kevin P. Thompson, Apr 26 2022: (Start)
a(12) >= 765.
795 and 949 are also terms in this sequence. (End)

Examples

			7 is in this sequence because 4^7+7 = 37*443 and these two factors are prime.
19 is in this sequence because 4^19+19 = 11*24988900633 and these two factors are prime.

Links

Crossrefs

Cf. similar sequences listed in A252788.
Cf. A252657.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..130] | IsSemiprime(s) where s is 4^m+m];
  • Mathematica
    Select[Range[130], PrimeOmega[4^# + #]==2 &]
  • PARI
    main(m)=select(m->bigomega(4^m + m)==2, vector(m, i, i)); \\ Anders Hellström, Aug 14 2015

Extensions

a(6)-a(9) from Carl Schildkraut, Aug 14 2015
a(10)-a(11) from Kevin P. Thompson, Apr 26 2022

A252790 Numbers m such that 5^m + m is a semiprime.

Original entry on oeis.org

1, 4, 8, 17, 144, 154, 298, 572, 732
Offset: 1

Views

Author

Vincenzo Librandi, Dec 24 2014

Keywords

Comments

a(8) > 413. - Carl Schildkraut, Aug 14 2015
a(10) >= 766. - Kevin P. Thompson, May 01 2022

Examples

			1 is in this sequence because 5^1+1 = 2*3 is semiprime.
8 is in this sequence because 5^8+8 = 3*130211 and these two factors are prime.

Links

Crossrefs

Cf. similar sequences listed in A252788.
Cf. A252658.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..110] | IsSemiprime(s) where s is 5^m+m];
  • Mathematica
    Select[Range[413], PrimeOmega[5^# + #]==2 &]
  • PARI
    main(m)=select(m->bigomega(5^m + m)==2,vector(m,i,i)); \\ Anders Hellström, Aug 14 2015

Extensions

a(5)-a(7) from Carl Schildkraut, Aug 14 2015
a(8)-a(9) from Kevin P. Thompson, May 01 2022

A252791 Numbers m such that 6^m + m is a semiprime.

Original entry on oeis.org

2, 3, 5, 7, 11, 23, 41, 55, 73, 91, 131, 199, 221, 287
Offset: 1

Views

Author

Vincenzo Librandi, Dec 25 2014

Keywords

Comments

From Kevin P. Thompson, May 01 2022: (Start)
a(15) >= 335.
391, 443, 607, 683, 737, and 745 are also terms in this sequence. (End)

Examples

			2 is in this sequence because 6^2+2 = 2*19 is semiprime.
7 is in this sequence because 6^7+7 = 271*1033 and these two factors are prime.

Links

Crossrefs

Cf. similar sequences listed in A252788.
Cf. A252659.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..90] | IsSemiprime(s) where s is 6^m+m];
  • Mathematica
    Select[Range[90], PrimeOmega[6^# + #]==2 &]

Extensions

a(10)-a(14) by Luke March, Jul 08 2015

A252792 Numbers m such that 7^m + m is a semiprime.

Original entry on oeis.org

2, 3, 6, 12, 15, 16, 30, 54, 244, 850, 1488
Offset: 1

Views

Author

Vincenzo Librandi, Dec 25 2014

Keywords

Examples

			2 is in this sequence because 7^2+2 = 3*17 is semiprime.
6 is in this sequence because 7^6+6 = 5*23531 and these two factors are prime.

Crossrefs

Cf. similar sequences listed in A252788.
Cf. A252660.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..600] | IsSemiprime(s) where s is 7^m+m];
  • Mathematica
    Select[Range[600], PrimeOmega[7^# + #]==2 &]

Extensions

a(9) from Carl Schildkraut, Aug 14 2015
a(10) from Kevin P. Thompson, Apr 25 2022
a(11) from Charles R Greathouse IV, Apr 25 2022

A252793 Numbers m such that 8^m + m is a semiprime.

Original entry on oeis.org

1, 3, 5, 7, 11, 15, 21, 25, 75, 107, 221, 257, 273
Offset: 1

Views

Author

Vincenzo Librandi, Dec 25 2014

Keywords

Comments

Next terms: 347?, 479, 521, 551, .... - Charles R Greathouse IV, Aug 17 2015

Crossrefs

Cf. similar sequences listed in A252788.
Cf. A252661.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..70] | IsSemiprime(s) where s is 8^m+m];
  • Mathematica
    Select[Range[70], PrimeOmega[8^# + #]==2 &]
  • PARI
    is(n)=bigomega(8^n+n)==2 \\ Charles R Greathouse IV, Aug 14 2015

Formula

1 is in this sequence because 8^1+1 = 3*3 is semiprime.
7 is in this sequence because 8^7+7 = 3*699053 and these two factors are prime.

Extensions

a(9)-a(10) from Luke March, Jul 26 2015
a(11) from Carl Schildkraut, Aug 14 2015
a(12)-a(13) from Charles R Greathouse IV, Aug 17 2015

A252794 Numbers m such that 9^m + m is a semiprime.

Original entry on oeis.org

1, 5, 68, 85, 86, 92, 136
Offset: 1

Views

Author

Vincenzo Librandi, Dec 27 2014

Keywords

Comments

a(8) > 435. - Carl Schildkraut, Aug 14 2015

Examples

			1 is in this sequence because 9^1+1 = 2*5 is semiprime.
5 is in this sequence because 9^5+5 = 2*29527 and these two factors are prime.

Crossrefs

Cf. similar sequences listed in A252788.
Cf. A252662.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..435] | IsSemiprime(s) where s is 9^m+m];
  • Mathematica
    Select[Range[435], PrimeOmega[9^# + #]==2 &]

Extensions

a(4)-a(7) from Carl Schildkraut, Aug 14 2015

A252795 Numbers m such that 10^m + m is a semiprime.

Original entry on oeis.org

3, 7, 37, 43, 49, 51, 57, 73, 127
Offset: 1

Views

Author

Vincenzo Librandi, Dec 27 2014

Keywords

Comments

a(10) >= 217. - Hugo Pfoertner, Aug 06 2019
574 and 601 are also terms in this sequence. - Kevin P. Thompson, May 02 2022

Examples

			3 is in this sequence because 10^3+3 = 17*59 is semiprime.
7 is in this sequence because 10^7+7 = 941*10627 and these two factors are prime.

Links

Crossrefs

Cf. similar sequences listed in A252788.
Cf. A089379, A252663.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..70] | IsSemiprime(s) where s is 10^m+m];
  • Mathematica
    Select[Range[70], PrimeOmega[10^# + #]==2 &]
  • PARI
    is(n)=bigomega(10^n + n)==2 \\ Anders Hellström, Aug 15 2015

Extensions

a(8) from Carl Schildkraut, Aug 15 2015
Missing a(8) term added by Kevin P. Thompson, May 02 2022
Showing 1-8 of 8 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.