A162489 Least y such that x^y + y^x is prime, for x = A162488(n).

2, 2, 2, 2, 5, 15, 2, 33, 7, 3, 21, 8, 34, 9, 80, 56, 67, 9, 32, 65, 45, 133, 98, 36, 51, 157, 76, 214, 200, 87, 91, 111, 122, 342, 20, 142, 364, 289, 9, 184, 98, 423, 365, 20, 56, 441, 329, 8, 234, 234, 157, 291, 91, 379, 98, 464, 518, 325, 32, 654, 87, 634, 34, 21, 443

Offset: 1

Author

M. F. Hasler, Jul 04 2009

Keywords

• nonn

Comments

Sequences A162488 and A162490 list the corresponding x values and primes.

See there and the main entry A094133 for more information, links and references.

Examples

			The least x such that x^y + y^x is prime for some x>y>1 is A162488(1)=3, the smallest such y is a(1)=2, yielding the prime A162490(1) = 9 + 8 = 17.
		

Crossrefs

Cf. A094133, A162486, A162487, A162488, A162490.

Programs

Mathematica

lst = {}; Do[ If[ PrimeQ[x^y + y^x], AppendTo[lst, {x, y}]], {x, 3, 750}, {y, 2, x - 1}]; Transpose[ lst][[2]] (* Robert G. Wilson v, Aug 17 2009 *)

PARI

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

Formula

a(n)^A162488(n)+A162488(n)^a(n) = A162490(n)

Extensions

More terms from Robert G. Wilson v, Aug 17 2009