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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 13:24 EDT 2022. Contains 354883 sequences. (Running on oeis4.)