login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A285888
Numbers n such that (1 + n)^n + (-n)^n is prime.
3
0, 2, 3, 4, 5, 7, 167
OFFSET
1,2
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)
LINKS
J. S. Gerasimov, x^(y + 1) - y^x, SeqFan list, Aug 18 2014.
EXAMPLE
4 is in this sequence because (1 + 4)^4 + (-4)^4 = 881 is prime.
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
PROG
(Magma) [n: n in [0..170]| IsPrime((n+1)^n + (-n)^n)];
(PARI) is(n)=ispseudoprime((n+1)^n+(-n)^n) \\ Charles R Greathouse IV, Apr 28 2017
CROSSREFS
Supersequence of A098463.
Sequence in context: A259389 A277217 A259384 * A028986 A327324 A063948
KEYWORD
nonn,more
AUTHOR
STATUS
approved