

A094133


Primes of form x^y + y^x, for x,y > 1, known as Leyland primes.


16



17, 593, 32993, 2097593, 8589935681, 59604644783353249, 523347633027360537213687137, 43143988327398957279342419750374600193, 4318114567396436564035293097707729426477458833, 5052785737795758503064406447721934417290878968063369478337
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OFFSET

1,1


COMMENTS

Contains A061119 as a subsequence.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..48
A. Kulsha, The XYYXF project  Primes and PRPs.
A. Kulsha, Completely factored numbers x^y + y^x with 1 < y < x, sorted on x, then on y, for x < 101.
A. Kulsha, Completely factored numbers x^y + y^x with 1 < y < x, sorted on x, then on y, for 100 < x < 151.
P. Leyland, Primes and PRPs of the form x^y + y^x.
Ed Copeland and Brady Haran, Leyland Numbers  Numberphile (2014)


EXAMPLE

a(1) to a(10) are the 10 smallest primes of this form: 3^2+2^3, 9^2+2^9, 15^2+2^15, 21^2+2^21, 33^2+2^33, 24^5+5^24, 56^3+3^56, 32^15+15^32, 54^7+7^54, 38^33+33^38.


MATHEMATICA

a = {}; Do[Do[k = m^n + n^m; If[PrimeQ[k], AppendTo[a, k]], {m, 2, n}], {n, 2, 100}]; Union[a] (* Artur Jasinski *)


PROG

(PARI) f(x)=my(L=log(x)); L/lambertw(L) \\ finds y such that y^y == x
list(lim)=my(v=List()); for(x=2, f(lim/2), my(y=x+1, t); while((t=x^y+y^x)<=lim, if(ispseudoprime(t), listput(v, t)); y+=2)); Set(v) \\ Charles R Greathouse IV, Oct 28 2014


CROSSREFS

Sequence in context: A041544 A202407 A009709 * A162490 A142744 A219090
Adjacent sequences: A094130 A094131 A094132 * A094134 A094135 A094136


KEYWORD

nonn


AUTHOR

Lekraj Beedassy, May 04 2004


EXTENSIONS

Corrected and extended by Jens Kruse Andersen, Oct 26 2007


STATUS

approved



