

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)).


15



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]
Conjecture: For d > 11, 10^(d1)+(d1)^10 is the smallest (base ten) ddigit term.  Hans Havermann, May 21 2018
(i) For each n > 0, we have a(n) <= p+1 < a(n+1) for some prime p.
(ii) a(n) < p < a(n+1) for some prime p, except that the interval (a(5), a(6)) = (54, 57) contains no prime. (End)


REFERENCES

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


LINKS



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


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.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



