A162488 Numbers x such that x^y + y^x is prime, for some y>1, y

3, 9, 15, 21, 24, 32, 33, 38, 54, 56, 68, 69, 75, 76, 81, 87, 114, 122, 135, 144, 158, 160, 171, 185, 206, 214, 215, 235, 237, 248, 318, 322, 333, 343, 357, 387, 405, 406, 422, 425, 435, 436, 444, 471, 477, 488, 510, 519, 545, 557, 580, 590, 636, 648, 663, 675

Offset: 1

Author

M. F. Hasler, Jul 04 2009

Keywords

• nonn

Comments

This sequence lists the values occurring in A162486.

Sequences A162489 and A162490 list the corresponding (smallest possible) y values and primes.

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

Some terms could appear more than once, such as 114, 318 & 590. - Robert G. Wilson v, Aug 17 2009

Examples

			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.
		

Crossrefs

Cf. A094133, A160044 (complement of this sequence), A162486 - A162490.

Programs

Mathematica

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 *)

PARI

for(i=3,999,for(j=2,i-1,is/*pseudo*/prime(i^j+j^i)|next;print1(i", ");break))

Formula

a(n)^A162489(n) + A162489(n)^a(n) = A162490(n).

Extensions

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