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Least prime of the form x^y+y^x with x = A162488(n) > y > 1.
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%I #8 Feb 07 2025 14:25:45

%S 17,593,32993,2097593,59604644783353249,

%T 43143988327398957279342419750374600193,8589935681,

%U 5052785737795758503064406447721934417290878968063369478337

%N Least prime of the form x^y+y^x with x = A162488(n) > y > 1.

%C Sequences A162488 and A162489 list the corresponding x and y values.

%C Sequence A094133 lists these primes ordered by their size (without multiplicity). See there for more information, links and references.

%F a(n) = A162488(n)^A162489(n) + A162489(n)^A162488(n).

%e The least x such that x^y+y^x is prime for some x>y>1 is A162488(1)=3, for y=A162489(1)=2, yielding the prime a(1) = 9 + 8 = 17.

%o (PARI) for(i=3,999,for(j=2,i-1,isprime(i^j+j^i)||next;print1(i^j+j^i", ");break))

%Y Cf. A094133, A162486 - A162489.

%K nonn

%O 1,1

%A _M. F. Hasler_, Jul 04 2009