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A123036 Prime sums of 7 positive 5th powers.

%I A123036 #13 Jun 13 2016 04:15:08
%S A123036 7,131,193,311,373,491,733,857,1061,1123,1217,1279,1303,1427,1459,
%T A123036 1607,1787,2029,2053,2357,3169,3373,3677,3739,3833,3919,4099,4583,
%U A123036 5153,5419,5903,6317,6379,6473,7043,7309,7793,7937,8117,8179,8297,8363,8539,8543,8867
%N A123036 Prime sums of 7 positive 5th powers.
%C A123036 Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584}.
%C A123036 There must be an odd number of odd terms in the sum, either seven odd (as with 7 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5), two even and 5 odd terms (as with 311 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 3^5), four even and 3 odd terms (as with 131 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 and 373 = 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5) or six even terms and one odd term (as with 193 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.
%H A123036 Giovanni Resta, <a href="/A123036/b123036.txt">Table of n, a(n) for n = 1..10000</a>
%F A123036 A000040 INTERSECTION A003352.
%e A123036 a(1) = 7 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5.
%e A123036 a(2) = 131 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5.
%e A123036 a(3) = 193 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
%e A123036 a(4) = 311 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 3^5.
%e A123036 a(5) = 373 = 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5.
%t A123036 Take[Union[Select[Total/@Tuples[Range[8]^5,7],PrimeQ]],50] (* _Harvey P. Dale_, May 08 2012 *)
%Y A123036 Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351, A003352.
%K A123036 easy,nonn
%O A123036 1,1
%A A123036 _Jonathan Vos Post_, Sep 24 2006
%E A123036 More terms from _Harvey P. Dale_, May 08 2012