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 A094133 Leyland primes: 3, together with primes of form x^y + y^x, for x>y>1. 19
 3, 17, 593, 32993, 2097593, 8589935681, 59604644783353249, 523347633027360537213687137, 43143988327398957279342419750374600193, 4318114567396436564035293097707729426477458833, 5052785737795758503064406447721934417290878968063369478337 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Contains A061119 as a subsequence. LINKS Charles R Greathouse IV and Hans Havermann (Charles R Greathouse IV to 49), Table of n, a(n) for n = 1..100 Ed Copeland and Brady Haran, Leyland Numbers - Numberphile (2014) A. Kulsha, The XYYXF project - Primes and PRPs. P. Leyland, Primes and PRPs of the form x^y + y^x EXAMPLE 2^1+1^2, 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. MAPLE N:= 10^100: # to get all terms <= N A:= {3}: for n from 2 while 2*n^n < N do   for k from n+1 do if igcd(n, k)=1 then      a:= n^k + k^n;      if a > N then break fi;      if isprime(a) then A:= A union {a} fi fi;   od od: A; # if using Maple 11 or earlier, uncomment the next line # sort(convert(A, list)); # Robert Israel, Apr 13 2015 MATHEMATICA a = {3}; 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 Cf. A061119 (primes where one of x,y is 2), A064539 (non-2 values where one of x,y is 2), A253471 (non-3 values where one of x,y is 3), A073499 (subset listing y where x = y+1), A076980 (Leyland numbers). Sequence in context: A128300 A001601 A061119 * A049985 A126579 A270816 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 Edited by Hans Havermann, Apr 10 2015 STATUS approved

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