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

1,1

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

Example

61 = 5^2 + 2^2 + 2^5.
89 = 4^3 + 3^2 + 2^4.

Mathematica

Take[Select[Intersection[Flatten[Table[x^y+y^z+z^x, {x, 2, 60}, {y, 2, 60}, {z, 2, 60}]]], PrimeQ[ # ]&], 40]

Prog

(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

Crossrefs

Cf. A094133 (primes of form x^y + y^x), A386892.

Sequence in context: A186457 A103812 A047272 * A309180 A038856 A144970

Adjacent sequences: A123204 A123205 A123206 * A123208 A123209 A123210

Keyword

nonn

Author

Alexander Adamchuk, Oct 04 2006

Extensions

a(32)-a(35) from Michael S. Branicky, Jul 11 2025

Status

approved