

A076980


Leyland numbers: 3, together with numbers expressible as n^k + k^n nontrivially, i.e. n,k > 1 (to avoid n = (n1)^1 +1^(n1)).


10



3, 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 refer to these numbers in reference to 2638^4405 + 4405^2638, which was then the largest known prime of this form.  Alonso del Arte, Apr 05 2006 [Comment amended by N. J. A. Sloane, Apr 06 2015]


REFERENCES

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


LINKS

T. D. Noe and Hans Havermann (T. D. Noe to 1001), Table of n, a(n) for n = 1..5000
Wikipedia, Leyland number.


EXAMPLE

a(9) = 177 because we can write 177 = 2^7 + 7^2


MAPLE

N:= 10^7: # to get all terms <= N
A:= {3}:
for n from 2 to floor(N^(1/2)) do
for k from 2 do
a:= n^k + k^n;
if a > N then break fi;
A:= A union {a};
od
od:
A; # if using Maple 11 or earlier, uncomment the next line
# sort(convert(A, set)); # Robert Israel, Apr 13 2015


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: A105163 A011850 A141422 * A001580 A002625 A027181
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



