A240532 Numbers k such that (k+1)^(k-1) - k is prime.

3, 5, 8, 17, 30, 66, 86, 100, 122, 160, 2282, 6508

Offset: 1

Author

Vincenzo Librandi, Apr 13 2014

Keywords

• nonn
• more
• hard

Comments

a(13) >= 8394. - J.W.L. (Jan) Eerland, Dec 23 2021

a(13) >= 20000. - Michael S. Branicky, Sep 01 2024

Examples

			3 is in the sequence since (3+1)^(3-1) - 3 = 4^2 - 3 = 13 is prime.
		

Crossrefs

Cf. A238378.

Programs

Magma

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

Mathematica

Select[Range[0, 500], PrimeQ[(# + 1)^(# - 1) - #] &]
n=0;Monitor[Parallelize[While[True,If[PrimeQ[(n+1)^(n-1)-n],Print[n]];n++];n],n] (* J.W.L. (Jan) Eerland, Dec 23 2021 *)

PARI

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

Python

from sympy import isprime
def afind(limit, startk=1):
    for k in range(startk, limit+1):
        if isprime((k+1)**(k-1) - k): print(k, end=", ")
afind(200) # Michael S. Branicky, Aug 17 2021

Extensions

a(11) from Michael S. Branicky, Aug 17 2021