A085319 - OEIS

%I #16 Nov 26 2014 14:42:15

%S 3,307,487,9043,16871,17293,17863,23057,32359,32801,33857,36739,40787,

%T 43669,50599,59051,59113,62417,65537,76099,101267,104149,107777,

%U 135893,160073,161053,164419,249107,249857,256609,259733,266663,338909,340649

%N Primes which are the sum of three 5th powers.

%C 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

%H Vladimir Joseph Stephan Orlovsky, <a href="/A085319/b085319.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 3 = 1^5 + 1^5 + 1^5.

%e a(2) = 307 = 2^5 + 2^5 + 3^5.

%e a(3) = 487 = 1^5 + 3^5 + 3^5.

%e a(4) = 9043 = 3^5 + 4^5 + 6^5.

%e a(5) = 16871 = 2^5 + 2^5 + 7^5.

%e a(6) = 17293 = 3^5 + 3^5 + 7^5.

%t 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 *)

%t Select[Prime[Range[2,30000]],Length[PowersRepresentations[#,3,5]]>0&] (* _Harvey P. Dale_, Nov 26 2014 *)

%Y Cf. A003348, A007490, A085318.

%Y Cf. A000040, A000584, A003336, A003347.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 01 2003

%E A123032 was identical. - _T. D. Noe_, Jul 15 2011