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A123035 Prime sums of 6 positive 5th powers.

%I A123035 #15 Jun 13 2016 04:13:42
%S A123035 37,521,1091,1153,1997,2083,2239,3137,3559,4129,4153,4457,4637,5449,
%T A123035 6199,7253,8147,8573,9319,9323,10069,10463,11959,14029,15083,15649,
%U A123035 16649,16843,16883,17327,17389,17569,17959,18077,18773,18803,19373,20029
%N A123035 Prime sums of 6 positive 5th powers.
%C A123035 Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584}.
%C A123035 There must be an odd number of odd terms in the sum, either one even and 5 odd terms (as with 37 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 and 521 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5), three even and 3 odd terms (as with 1091 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 4^5) or five even terms and one odd term (as with 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 4^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.
%H A123035 Giovanni Resta, <a href="/A123035/b123035.txt">Table of n, a(n) for n = 1..10000</a>
%F A123035 A000040 INTERSECTION A003351.
%e A123035 a(1) = 37 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5.
%e A123035 a(2) = 521 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5.
%e A123035 a(3) = 1091 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 4^5.
%e A123035 a(4) = 1153 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 4^5.
%t A123035 up = 10^6; q = Range[up^(1/5)]^5; a = {0}; Do[b = Select[ Union@ Flatten@Table[e + a, {e, q}], # <= up &]; a = b, {k, 6}]; Select[a, PrimeQ] (* _Giovanni Resta_, Jun 13 2016 *)
%Y A123035 Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351.
%K A123035 nonn
%O A123035 1,1
%A A123035 _Jonathan Vos Post_, Sep 24 2006
%E A123035 More terms from _Max Alekseyev_, Sep 24 2011