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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS FORMULA a(n)^A162489(n) + A162489(n)^a(n) = A162490(n). EXAMPLE The least x such that x^y + y^x is prime for some y>1, y a(4)=21 such that x^y + y^x is prime for some y1, 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. 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 *) PROG (PARI) for(i=3, 999, for(j=2, i-1, is/*pseudo*/prime(i^j+j^i)|next; print1(i", "); break)) CROSSREFS Cf. A094133, A160044 (complement of this sequence), A162486 - A162490. Sequence in context: A261190 A282031 A307202 * A324298 A194041 A029506 Adjacent sequences:  A162485 A162486 A162487 * A162489 A162490 A162491 KEYWORD nonn AUTHOR M. F. Hasler, Jul 04 2009 EXTENSIONS More terms from Robert G. Wilson v, Aug 17 2009 STATUS approved

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)