A085682 -id:A085682 - cp's OEIS frontend

A098463 Numbers k such that A055869(k) = (k+1)^k - k^k is prime.

2, 3, 5, 7, 167

Offset: 1

Hugo Pfoertner, Sep 14 2004

The next term is > 5000.

			a(2) = 3 because (3+1)^3 - 3^3 = 4^3 - 3^3 = 64 - 27 = 37 is prime.

Cf. A055869 ((n+1)^n-n^n), A085682 (k^k-(k-1)^k is prime).

[n: n in [0..190]| IsPrime((n+1)^n -n^n)]; // Vincenzo Librandi, Jun 22 2014

Select[Range[300], PrimeQ[(#+1)^#-#^#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2011 *)

isok(k) = ispseudoprime((k+1)^k - k^k); \\ Jinyuan Wang, Mar 19 2020

A086877 Primes of the form (k+1)^k - k^k.

Original entry on oeis.org

5, 37, 4651, 1273609

Offset: 1

Cino Hilliard, Aug 21 2003

nonn

Sean A. Irvine, Table of n, a(n) for n = 1..5

The values of k are in A098463.
Primes in A055869.
Cf. A085682.

f(n) = for(x=1,n,y=(x+1)^x-x^x; if(isprime(y),print1(y, ", ")))

a(n) = A055869(A098463(n)). - Elmo R. Oliveira, Feb 19 2025

A255730 Numbers k such that k^k - (k-1)^k + k is prime.

Original entry on oeis.org

1, 2, 4, 16, 52, 80

Offset: 1

Vincenzo Librandi, Mar 13 2015

a(6) corresponds to a prime having 153 digits.
If it exists, a(7) > 5000.
k does not have the form 20m+2 (which leads to a multiple of 5) or 42m+26 (which leads to a multiple of 7).
If it exists, a(7) > 20000. - Michael S. Branicky, Oct 09 2024

			4 is in the sequence because 4^4 - 3^4 + 4 = 179 is prime.

Cf. A085682.

[n: n in [0..500] |IsPrime(n^n - (n-1)^n + n)];

Select[Range[1000], PrimeQ[#^# - (# - 1)^# + #] &]

is(n)=ispseudoprime(n^n-(n-1)^n+n) \\ Charles R Greathouse IV, Jun 13 2017

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A098463 Numbers k such that A055869(k) = (k+1)^k - k^k is prime.

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A086877 Primes of the form (k+1)^k - k^k.

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A255730 Numbers k such that k^k - (k-1)^k + k is prime.

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Magma

Mathematica

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