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 1-7 of 7 results.

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.

Links

Crossrefs

Cf. A001358, A007647, A064748, A216376.
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

A242204 Numbers n such that n*4^n+1 is semiprime.

Original entry on oeis.org

2, 6, 8, 9, 13, 15, 25, 36, 37, 63, 66, 72, 73, 85, 205, 333, 430
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2014

Keywords

Comments

The semiprimes of this form are: 33, 24577, 524289, 2359297, 872415233, 16106127361, 28147497671065601, 170005193383307227693057, 698910239464707491627009, ...
a(18) >= 547. - Hugo Pfoertner, Aug 05 2019

Links

Crossrefs

Cf. similar sequences listed in A242203.
Cf. A007646, A050915.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..110] | IsSemiprime(s) where s is n*4^n+1];
  • Mathematica
    Select[Range[120], PrimeOmega[# 4^# + 1] == 2 &]

Extensions

a(15)-a(17) from Luke March, Aug 13 2015

A242205 Numbers n such that n*5^n+1 is semiprime.

Original entry on oeis.org

1, 2, 4, 16, 21, 40, 76, 113, 153, 288
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2014

Keywords

Comments

The semiprimes of this form are 6, 51, 2501, 2441406250001, 10013580322265626, 363797880709171295166015625001, ...
a(11) >= 1006. - Hugo Pfoertner, Aug 05 2019

Links

Crossrefs

Cf. similar sequences listed in A242203.
Cf. A050916.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..90] | IsSemiprime(s) where s is n*5^n+1];
  • Mathematica
    Select[Range[90], PrimeOmega[# 5^# + 1] == 2 &]

Extensions

a(8)-a(10) from Luke March, Aug 13 2015

A242269 Numbers n such that n*6^n+1 is semiprime.

Original entry on oeis.org

3, 5, 11, 12, 18, 20, 21, 24, 25, 35, 43, 45, 53, 58, 61, 71, 73, 75, 123, 124, 140, 147, 157, 205, 208, 233, 243, 245, 293, 301
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2014

Keywords

Comments

The semiprimes of this form are: 649, 38881, 3990767617, 26121388033, 1828079220031489, 73123168801259521, 460675963447934977,...
464 is definitely in this sequence, however 436 may or may not be. - Carl Schildkraut, Aug 28 2015
A continuation in the range 302 ... 1000 would use all terms without "?" and potentially ?-marked terms corresponding to composites with unknown factorization: 436?, 464, 511?, 512, 613, 662?, 720, 730, 802?, 865?, 943. - Hugo Pfoertner, Aug 05 2019

Links

Crossrefs

Cf. similar sequences listed in A242203.
Cf. A050917, A242176.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..435] | IsSemiprime(s) where s is n*6^n+1];
  • Mathematica
    Select[Range[435], PrimeOmega[# 6^# + 1] == 2 &]
  • PARI
    is(n)=bigomega(n*6^n+1)==2 \\ Anders Hellström, Aug 28 2015

Extensions

a(19)-a(30) from Carl Schildkraut, Aug 28 2015

A242270 Numbers k such that k*7^k+1 is semiprime.

Original entry on oeis.org

6, 8, 10, 14, 15, 60, 90, 114, 118, 204, 350, 390
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2014

Keywords

Comments

The semiprimes of this form are: 705895, 46118409, 2824752491, 9495123019887, 71213422649146, ...
a(13) >= 720. - Kevin P. Thompson, Apr 20 2022

Links

Crossrefs

Cf. similar sequences listed in A242203.
Cf. A050919, A242177.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..80] | IsSemiprime(s) where s is n*7^n+1];
  • Mathematica
    Select[Range[80], PrimeOmega[# 7^# + 1] == 2 &]
  • PARI
    is(k) = bigomega(k*7^k+1)==2;
for(k=0,120,if(k%4!=1,if(is(k),print1(k, ", ")))); \\ Jinyuan Wang, Apr 07 2019

Extensions

a(7)-a(9) from Jinyuan Wang, Apr 07 2019
a(10)-a(12) from Kevin P. Thompson, Apr 20 2022

A242271 Numbers n such that n*8^n+1 is semiprime.

Original entry on oeis.org

1, 2, 3, 9, 24, 32, 35, 51, 75, 234, 243, 392, 417, 472
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2014

Keywords

Comments

The semiprimes of this form are: 9, 129, 1537, 1207959553, 113336795588871485128705, 2535301200456458802993406410753, ...
a(15) >= 483. - Hugo Pfoertner, Aug 05 2019

Links

Crossrefs

Cf. similar sequences listed in A242203.
Cf. A064746, A242178.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..80] | IsSemiprime(s) where s is n*8^n+1];
  • Mathematica
    Select[Range[80], PrimeOmega[# 8^# + 1] == 2 &]

Extensions

a(10)-a(14) from Hugo Pfoertner and Daniel Suteu, Aug 05 2019

A242272 Numbers n such that n*9^n+1 is semiprime.

Original entry on oeis.org

1, 8, 12, 16, 20, 50, 208, 254, 282, 342, 350, 386
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2014

Keywords

Comments

The semiprimes of this form are: 10, 344373769, 3389154437773, 29648323021629457, 243153309181138576021, ...
a(13) >= 512. - Hugo Pfoertner, Aug 05 2019

Links

Crossrefs

Cf. similar sequences listed in A242203.
Cf. A064747.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..70] | IsSemiprime(s) where s is n*9^n+1];
  • Mathematica
    Select[Range[70], PrimeOmega[# 9^# + 1] == 2 &]

Extensions

a(7)-a(12) from Hugo Pfoertner, Aug 05 2019
Showing 1-7 of 7 results.

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