A285888 Numbers n such that (1 + n)^n + (-n)^n is prime.

0, 2, 3, 4, 5, 7, 167

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 27 2017

Keywords

• nonn
• more

Comments

The next term, if it exists, is > 10000. - Hugo Pfoertner, Jan 06 2020

The associated primes are: 13, 37, 881, 4651, 1273609, ...

From Robert Israel, Apr 28 2017: (Start)

All terms other than 0 are primes or powers of 2.

Heuristically, this sequence might be expected to be finite. (End)

Examples

			4 is in this sequence because (1 + 4)^4 + (-4)^4 = 881 is prime.
		

Links

• J. S. Gerasimov, x^(y + 1) - y^x, SeqFan list, Aug 18 2014.

Crossrefs

Supersequence of A098463.

Cf. A243100, A285886, A285887.

Programs

Magma

[n: n in [0..170]| IsPrime((n+1)^n + (-n)^n)];

Maple

N:= 1000: # to get all terms <= N
cands:= select(isprime, {seq(i,i=3..N,2)}) union {0, seq(2^k, k=1..ilog2(N))}:
select(n -> isprime((1+n)^n + (-n)^n), cands); # Robert Israel, Apr 28 2017

PARI

is(n)=ispseudoprime((n+1)^n+(-n)^n) \\ Charles R Greathouse IV, Apr 28 2017