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%I #10 Jun 13 2016 08:34:04
%S 107,293,349,653,659,839,1013,1019,1223,1279,1409,1559,1583,1621,1801,
%T 1831,1949,2011,2129,2153,2309,2333,2339,2347,2371,2551,2699,2707,
%U 2731,2879,2917,3083,3121,3169,3191,3301,3331,3449,3457,3511,3541,3659,3691,3761,3847,4019,4027,4051
%N Prime sums of 14 positive 5th powers.
%H Giovanni Resta, <a href="/A123300/b123300.txt">Table of n, a(n) for n = 1..10000</a>
%F A000040 INTERSECTION A123295.
%e a(1) = 107 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5.
%e a(2) = 293 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
%e a(3) = 349 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 3^5.
%e a(4) = 653 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5.
%t up = 5000; q = Range[up^(1/5)]^5; a={0}; Do[b = Select[Union@ Flatten@ Table[e + a, {e, q}], # <= up &]; a = b, {k, 14}]; Select[a, PrimeQ] (* _Giovanni Resta_, Jun 12 2016 *)
%Y Cf. A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353, A003354, A003355, A003356, A003357, A123294-A123299.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 25 2006
%E More terms from _Harvey P. Dale_, Jan 01 2015
%E 4 missing terms from _Giovanni Resta_, Jun 12 2016
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