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A162488 Numbers x such that x^y + y^x is prime, for some y>1, y<x. 10


%S 3,9,15,21,24,32,33,38,54,56,68,69,75,76,81,87,114,122,135,144,158,

%T 160,171,185,206,214,215,235,237,248,318,322,333,343,357,387,405,406,

%U 422,425,435,436,444,471,477,488,510,519,545,557,580,590,636,648,663,675

%N Numbers x such that x^y + y^x is prime, for some y>1, y<x.

%C This sequence lists the values occurring in A162486.

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

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

%C Some terms could appear more than once, such as 114, 318 & 590. - _Robert G. Wilson v_, Aug 17 2009

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

%e 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.

%e 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.

%t 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 *)

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

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

%K nonn

%O 1,1

%A _M. F. Hasler_, Jul 04 2009

%E More terms from _Robert G. Wilson v_, Aug 17 2009

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Last modified April 19 09:16 EDT 2019. Contains 322241 sequences. (Running on oeis4.)