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 1-3 of 3 results.

A114973 Numbers n such that 5^n + n^5 is a semiprime.

Original entry on oeis.org

1, 2, 4, 6, 8, 9, 84, 288, 628
Offset: 1

Views

Author

Zak Seidov, Feb 22 2006

Keywords

Comments

a(10) >= 868. - Hugo Pfoertner, Jul 28 2019

Examples

			2 is OK because 5^2 + 2^5 = 25 + 32 = 57 = 3*19 (semiprime).
		

Crossrefs

Programs

  • Magma
    IsSemiprime:=func< n|&+[k[2]: k in Factorization(n)] eq 2 >; [n: n in [1..85]|IsSemiprime(5^n+n^5)]; // Vincenzo Librandi, Dec 16 2010
  • Mathematica
    Select[Range[100],PrimeOmega[5^# + #^5]==2&] (* Vincenzo Librandi, May 21 2014 *)

Extensions

a(8), a(9) from Hugo Pfoertner, Jul 28 2019

A114974 Numbers n such that 7^n + n^7 is a semiprime.

Original entry on oeis.org

2, 12, 16, 18, 30, 39, 160, 214, 235, 408
Offset: 1

Views

Author

Zak Seidov, Feb 22 2006

Keywords

Comments

627 and 748 are sequence terms < 1100. a(11) >= 510. Unknown factorization also for 622 and 790. - Hugo Pfoertner, Jul 28 2019

Examples

			2 is in the sequence because 7^2 + 2^7 = 177 = 3*59 (semiprime).
12 is in the sequence because 7^12 + 12^7 = 13*1067470693 (semiprime). [_Vincenzo Librandi_, Dec 16 2010]
		

Crossrefs

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..85] | IsSemiprime(7^n+n^7)] // Vincenzo Librandi, Dec 16 2010

Extensions

Corrected (inserted 12) from Vincenzo Librandi, Dec 16 2010
a(7) from D. S. McNeil, Dec 16 2010
a(8)-a(10) from Luke March, Aug 03 2015

A114970 Numbers m such that 2^m + m^2 is a semiprime.

Original entry on oeis.org

5, 7, 17, 25, 43, 61, 69, 73, 105, 111, 117, 123, 135, 141, 171, 219, 231, 241, 309, 321, 543, 739, 795, 833, 975
Offset: 1

Views

Author

Zak Seidov, Feb 22 2006

Keywords

Comments

a(26) >= 1125. - Tyler Busby, Dec 27 2024

Examples

			2^5 + 5^2 = 32 + 25 = 57 = 3*19 (semiprime).
		

Crossrefs

Programs

  • Magma
    IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [1..175]|IsSemiprime(2^n+n^2)]; // Vincenzo Librandi, Dec 16 2010
  • Mathematica
    Select[Range[200], PrimeOmega[2^# + #^2]==2&] (* Vincenzo Librandi, May 21 2014 *)

Extensions

a(16)-a(21) from Luke March, Jul 27 2015
a(22) from Hugo Pfoertner, Jul 28 2019
a(23)-a(25) from Tyler Busby, Dec 27 2024
Showing 1-3 of 3 results.