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 1-4 of 4 results.

A062500 Duplicate of A007965.

Original entry on oeis.org

1, 1, 118, 13983, 48667074, 13055867207, 232630103648534, 144115171092292831
Offset: 1

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Author

Keywords

A140893 a(n) = prime(n)^prime(n+1) - prime(n+1)^prime(n).

Original entry on oeis.org

-1, 118, 61318, 1957839572, 32730551749894, 8640511341348431996, 233592048827366522661214, 257755012474380136537664158772, 3091054326372819773383775097721670599074, 2141662167055484666186673758527328459608763158
Offset: 1

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Author

Juri-Stepan Gerasimov, Jul 07 2008

Keywords

Comments

a(n) > 0 for n>=2. - Robert Israel, Nov 02 2014
a(n) = A053089(n) - A078422(n). - Michel Marcus, Oct 10 2016

Examples

			n=1: a(1) = prime(1)^prime(1+1) - prime(1+1)^prime(1) = 2^3 - 3^2 = 8 - 9 = -1.
n=3: a(3) = prime(3)^prime(4) - prime(4)^prime(3) = 5^7 - 7^5 = 78125 - 16807 = 61318.
		

Crossrefs

Programs

  • Magma
    [NthPrime(n)^NthPrime(n+1)-NthPrime(n+1)^NthPrime(n): n in [1..10]]; // Vincenzo Librandi, Nov 02 2014
  • Maple
    seq(ithprime(i)^ithprime(i+1)-ithprime(i+1)^ithprime(i), i=1..20); # Robert Israel, Nov 02 2014
  • Mathematica
    Array[Prime[ # ]^Prime[ #+1]-Prime[ #+1]^Prime[ # ]&,16] (* Vladimir Joseph Stephan Orlovsky, Oct 11 2009 *)

Extensions

Corrected and extended by Vladimir Joseph Stephan Orlovsky, Oct 11 2009
a(10) from Vincenzo Librandi, Nov 02 2014

A140892 a(n) = (n-1)^F(n) - F(n)^(n-1), where F(n) = A000045(n).

Original entry on oeis.org

-1, 0, 0, 0, 399, 357857, 13055867207, 558545862282195466, 5070602400912917604201018916608, 30432527221704537086371993251530170527181380482652674, 99999999999999999999999999999999999999999999999999999999999999999999968818280070033816399
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jul 07 2008

Keywords

Examples

			a(1) = (1-1)^F(1) - F(1)^(1-1) = 0^1 - 1^0 = 0 - 1 = -1;
a(4) = (4-1)^F(4) - F(4)^(4-1) = 3^3 - 3^3 = 27 - 27 = 0;
a(5) = (5-1)^F(5) - F(5)^(5-1) = 4^5 - 5^4 = 1024 - 625 = 399.
		

Crossrefs

Programs

  • Mathematica
    Table[(n-1)^Fibonacci[n] - Fibonacci[n]^(n-1), {n, 1, 12}] (* Georg Fischer, Apr 11 2023 *)

Formula

a(n) = (n-1)^A000045(n) - A000045(n)^(n-1). - Jonathan Vos Post, Jul 12 2008

Extensions

More terms from Jonathan Vos Post, Jul 12 2008
a(1) and a(7) corrected by Georg Fischer, Apr 11 2024

A262185 a(n) = n^prime(n!) - prime(n!)^n.

Original entry on oeis.org

-1, -1, -1, 1592126, 383123885216472214589586756787577295904684780483158303
Offset: 0

Views

Author

Altug Alkan, Sep 14 2015

Keywords

Comments

Inspired by A007965.

Examples

			For n = 1, a(n) = n^prime(n!) - prime(n!)^n = 1^2 - 2^1 = -1.
		

Crossrefs

Programs

  • Magma
    [n^NthPrime(Factorial(n)) - NthPrime(Factorial(n))^n: n in [0..6]]; // Vincenzo Librandi, Sep 15 2015
  • Mathematica
    Table[n^Prime[n!] - Prime[n!]^n, {n, 0, 4}] (* Michael De Vlieger, Sep 14 2015 *)
  • PARI
    a(n) = n^prime(n!) - prime(n!)^n;
    vector (6, n, a(n-1))
    

Formula

a(n) = n^A062439(n) - A062439(n)^n.
Showing 1-4 of 4 results.