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 video (2014).
Hans Havermann, Table of n (where known), Leyland index, number of digits in decimal representation, and (x,y) pair for all known solutions.
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
Paul Leyland, Primes and PRPs of the form x^y + y^x.
Norman Luhn, Leyland table, 1st kind.
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
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