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A123034 Prime sums of 5 positive 5th powers.

%I A123034 #16 Jun 13 2016 04:10:45
%S A123034 5,67,1301,1543,2113,2293,2777,3191,3253,3347,3371,3433,3613,4339,
%T A123034 5237,5417,5659,6229,6737,7307,7549,7873,8053,8537,8803,9377,9439,
%U A123034 9619,9857,10099,11177,11423,11927,12743,15797,15859,16811,17053,17183,18679,18919,19163
%N A123034 Prime sums of 5 positive 5th powers.
%C A123034 Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584}.
%C A123034 There must be an odd number of odd terms in the sum, either 5 odd terms (as with 5 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 and 16811 = 1^5 + 1^5 + 1^5 + 1^5 + 7^5), two even and 3 odd terms (as with 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 and 1301 = 1^5 + 1^5 + 2^5 + 3^5 + 4^5) or four even terms and one odd term (as with 3253 = 2^5 + 2^5 + 2^5 + 2^5 + 5^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.
%H A123034 Giovanni Resta, <a href="/A123034/b123034.txt">Table of n, a(n) for n = 1..10000</a>
%F A123034 A000040 INTERSECTION A003350.
%e A123034 a(1) = 5 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5.
%e A123034 a(2) = 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5.
%e A123034 a(3) = 1301 = 1^5 + 1^5 + 2^5 + 3^5 + 4^5.
%e A123034 a(4) = 1543 = 1^5 + 2^5 + 3^5 + 3^5 + 4^5.
%e A123034 a(5) = 2113 = 1^5 + 2^5 + 2^5 + 4^5 + 4^5.
%e A123034 a(6) = 3191 = 1^5 + 1^5 + 2^5 + 2^5 + 5^5.
%e A123034 a(7) = 4339 = 3^5 + 4^5 + 4^5 + 4^5 + 4^5.
%t A123034 Take[Select[Union[Total/@Tuples[Range[10]^5,5]],PrimeQ],60] (* _Harvey P. Dale_, Jul 21 2014 *)
%Y A123034 Cf. A000040, A000584, A003336, A003347, A003349, A003350.
%K A123034 easy,nonn
%O A123034 1,1
%A A123034 _Jonathan Vos Post_, Sep 24 2006
%E A123034 Corrected and extended by _Harvey P. Dale_, Jul 21 2014