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A076980 Leyland numbers: 3, together with numbers expressible as n^k + k^n nontrivially, i.e. n,k > 1 (to avoid n = (n-1)^1 +1^(n-1)). 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 12:25 EST 2016. Contains 278971 sequences.