A123207 Primes of the form x^y + y^z + z^x, for x,y,z > 1.
61, 89, 181, 401, 673, 773, 2089, 2557, 12497, 33049, 78857, 98057, 98929, 135329, 268921, 338323, 390721, 531989, 552241, 554233, 794881, 1954097, 2165089, 4204961, 5967161, 8389141, 9765757, 11423429, 17200609, 33555061, 35835953, 40356523, 48829699, 87863309, 268457417
Offset: 1
Keywords
Examples
61 = 5^2 + 2^2 + 2^5. 89 = 4^3 + 3^2 + 2^4.
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
- Andrew Howroyd, Table of n, x, y, z, a(n) for n = 1..1000
Programs
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Mathematica
Take[Select[Intersection[Flatten[Table[x^y+y^z+z^x,{x,2,60},{y,2,60},{z,2,60}]]],PrimeQ[ # ]&],40] -
PARI
upto(lim) = { my(L=List()); for(x=2, logint(lim,2), for(y=2, min(x,logint(lim,x)), for(z=2, min(x-1,logint(lim,y)), my(t=x^y+y^z+z^x); if(t<=lim && isprime(t), listput(L,t)) ))); Set(L) } \\ Andrew Howroyd, Aug 06 2025
Extensions
a(32)-a(35) from Michael S. Branicky, Jul 11 2025