[seqfan] Leyland Numbers

[Hans Havermann]

https://oeis.org/A076980

"numbers expressible as n^k + k^n nontrivially, i.e. n,k > 1 (to avoid n = (n-1)^1 +1^(n-1))"

The triviality condition excludes 3 (= 2^1 + 1^2), which strikes me as a useful initial term. For example, because 3 is also excluded from the Leyland primes (A094133), the comment therein that A094133 "contains A061119 as a subsequence" isn't really correct because A061119 includes 3.

I'm also looking at Alonso del Arte's 2006 comment that "Crandall & Pomerance named these numbers in honor of Paul Leyland, in reference to 2638^4405 + 4405^2638, the largest known prime of this form." I've had a look at Crandall & Pomerance's 2005 "Prime Numbers: A Computational Perspective" and the reference is:

"A sensational announcement in July 2004 by Franke, Kleinjung, Morain, and Wirth is that, thanks to fastECPP, the Leyland number 4405^2638 + 2638^4405, having 15071 decimal digits, is now proven prime."

It strikes me that they are called Leyland numbers *in spite of* the primality proof so I find this reference a little misleading. At any rate, there's a couple of larger proven-prime examples now known.