A248872 Numbers k such that k^k + k! + 1 is prime.

1, 2, 4, 28, 496

Offset

1,2

Comments

These primes are of the form: A000312(n) + A000142(n) + 1.

Note that 28 and 496 are perfect numbers (see A000396).

a(6) > 1500.

a(6) > 25000. - Michael S. Branicky, Nov 12 2024

Links

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

Example

For n = 1, 1^1 + 1! + 1 = 3, which is prime.
For n = 2, 2^2 + 2! + 1 = 4 + 2 + 1 = 7, which is prime.
For n = 4, 4^4 + 4! + 1 = 281, which is prime.

Mathematica

Select[Range[1500], PrimeQ[#^# + #! + 1]&]

Prog

(PARI) for(n=1, 10^3, if(ispseudoprime(n^n+n!+1), print1(n, ", "))) \\ Derek Orr, Mar 06 2015

Crossrefs

Cf. A000312 (n^n), A000142(n!).

Sequence in context: A062792 A102692 A292184 * A329102 A126580 A329063

Adjacent sequences: A248869 A248870 A248871 * A248873 A248874 A248875

Keyword

nonn,more,hard

Author

Waldemar Puszkarz, Mar 04 2015

Status

approved