

A076980


Leyland numbers: numbers expressible as n^k + k^n nontrivially, i.e. n,k > 1 (to avoid n = (n1)^1 +1^(n1)).


8



8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124, 1649, 2169, 2530, 4240, 5392, 6250, 7073, 8361, 16580, 18785, 20412, 23401, 32993, 60049, 65792, 69632, 93312, 94932, 131361, 178478, 262468, 268705, 397585, 423393, 524649, 533169
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OFFSET

1,1


COMMENTS

Crandall & Pomerance named these numbers in honor of Paul Leyland, in reference to 2638^4405 + 4405^2638, the largest known prime of this form.  Alonso del Arte, Apr 05 2006


REFERENCES

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2005


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000
Wikipedia, Leyland number.


EXAMPLE

a(7) = 177 because we can write 177 = 2^7 + 7^2


MATHEMATICA

Take[Sort[Flatten[Table[x^y + y^x, {x, 2, 100}, {y, x, 100}]]], 42]  Alonso del Arte, Apr 05 2006
nn=10^50; n=1; Union[Reap[While[n++; num=2*n^n; num<nn, Sow[num]; k=n; While[k++; num=n^k+k^n; num<nn, Sow[num]]]][[2, 1]]]


CROSSREFS

Prime subset of this sequence, A094133.
Sequence in context: A077221 A226601 A106648 * A209376 A159696 A049713
Adjacent sequences: A076977 A076978 A076979 * A076981 A076982 A076983


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Oct 23 2002


EXTENSIONS

More terms from Benoit Cloitre, Oct 24 2002
More terms from Alonso del Arte, Apr 05 2006


STATUS

approved



