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

1, 2, 4, 16, 52, 80

Offset: 1

Author

Vincenzo Librandi, Mar 13 2015

Keywords

• nonn
• more

Comments

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

Examples

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

Crossrefs

Cf. A085682.

Programs

Magma

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

Mathematica

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

PARI

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