

A085319


Primes which are the sum of three 5th powers.


6



3, 307, 487, 9043, 16871, 17293, 17863, 23057, 32359, 32801, 33857, 36739, 40787, 43669, 50599, 59051, 59113, 62417, 65537, 76099, 101267, 104149, 107777, 135893, 160073, 161053, 164419, 249107, 249857, 256609, 259733, 266663, 338909, 340649
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OFFSET

1,1


COMMENTS

Primes in the sumset {A000584 + A000584 + A000584}. There must be an odd number of odd terms in the sum, either 3 odd terms (as with 3 = 1^5 + 1^5 + 1^5 and 487 = 1^5 + 3^5 + 3^5 and 59051 = 1^5 + 1^5 + 9^5) or two even terms and one odd term (as with 307 = 2^5 + 2^5 + 3^5 and 9043 = 3^5 + 4^5 + 6^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.  Jonathan Vos Post, Sep 24 2006


LINKS

Vladimir Joseph Stephan Orlovsky, Table of n, a(n) for n = 1..1000


EXAMPLE

a(1) = 3 = 1^5 + 1^5 + 1^5.
a(2) = 307 = 2^5 + 2^5 + 3^5.
a(3) = 487 = 1^5 + 3^5 + 3^5.
a(4) = 9043 = 3^5 + 4^5 + 6^5.
a(5) = 16871 = 2^5 + 2^5 + 7^5.
a(6) = 17293 = 3^5 + 3^5 + 7^5.


MATHEMATICA

lim = 10^6; nn = Floor[(lim  2)^(1/5)]; t = {}; Do[p = i^5 + j^5 + k^5; If[p <= lim && PrimeQ[p], AppendTo[t, p]], {i, nn}, {j, i}, {k, j}]; t = Union[t] (* Vladimir Joseph Stephan Orlovsky and T. D. Noe, Jul 15 2011 *)
Select[Prime[Range[2, 30000]], Length[PowersRepresentations[#, 3, 5]]>0&] (* Harvey P. Dale, Nov 26 2014 *)


CROSSREFS

Cf. A003348, A007490, A085318.
Cf. A000040, A000584, A003336, A003347.
Sequence in context: A071525 A157583 A218361 * A123032 A132305 A074327
Adjacent sequences: A085316 A085317 A085318 * A085320 A085321 A085322


KEYWORD

nonn


AUTHOR

Labos Elemer, Jul 01 2003


EXTENSIONS

A123032 was identical.  T. D. Noe, Jul 15 2011


STATUS

approved



