This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(1)=1 because A162488(1)-A162489(1)=1=nonprime and A162488(1)+A162489(1)=5=prime; a(2)=7 because A162488(7)-A162489(7)=31=prime and A162488(7)+A162489(7)=35=nonprime.
a(1)=0 because 1^1+1^1=2=prime and 0=1-1; a(2)=1 because 1^2+2^1=3=prime and 1=2-1; a(3)=1 because 2^3+3^2 and 1=3-2; a(4)=7 because 2^9+9^2 and 7=9-2.
The least x such that x^y + y^x is prime for some y>1, y<x is a(1)=3, the smallest such y is a(1)=2, yielding the prime A162490(1) = 9 + 8 = 17. The least x > a(4)=21 such that x^y + y^x is prime for some y<x, y>1, is a(5)=24, yielding the prime A162490(5) for y=A162489(5)=5, while A162486(5)=33, yielding the smaller prime A094133(5)=8589935681 with y=A162487(5), comes only after a(6)=32.
lst = {}; Do[ If[ PrimeQ[x^y + y^x], AppendTo[lst, x]], {x, 3, 680}, {y, 2, x - 1}]; Union@ lst (* Robert G. Wilson v, Aug 17 2009 *)
for(i=3,999,for(j=2,i-1,is/*pseudo*/prime(i^j+j^i)|next;print1(i", ");break))
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.
for(i=3,999,for(j=2,i-1,isprime(i^j+j^i)||next;print1(i^j+j^i", ");break))
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