This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A123043 #11 Jun 13 2016 04:20:45
%S A123043 41,103,227,283,587,829,953,1009,1033,1399,1493,1523,1579,1759,2063,
%T A123043 2087,2243,2273,2633,2789,2969,3079,3203,3359,3407,3413,3469,3539,
%U A123043 3593,3929,4133,4157,4219,4289,4523,4679,4703,5101,5273,5851,6203,6389,6421,6569,6991
%N A123043 Prime sums of 10 positive 5th powers.
%C A123043 Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584}.
%C A123043 There must be an odd number of odd terms in the sum, either one even and nine odd (as with 41 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 and 283 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5), three even and seven odd (as with 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 and 587 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5), five even and 5 odd terms (as with 17939 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 7^5), seven even and 3 odd terms (as with 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5) or nine even terms and one odd term (as with 3413 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 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 A123043 Giovanni Resta, <a href="/A123043/b123043.txt">Table of n, a(n) for n = 1..10000</a>
%F A123043 A000040 INTERSECTION A003355.
%e A123043 a(1) = 41 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5.
%e A123043 a(2) = 103 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5.
%e A123043 a(3) = 227 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
%e A123043 a(4) = 283 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5.
%e A123043 a(5) = 587 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5.
%t A123043 up = 10^4; q = Range[up^(1/5)]^5; a = {0}; Do[b = Select[ Union@ Flatten@ Table[e + a, {e, q}], # <= up &]; a = b, {k, 10}]; Select[a, PrimeQ] (* _Giovanni Resta_, Jun 13 2016 *)
%Y A123043 Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353, A003354, A003355.
%K A123043 easy,nonn
%O A123043 1,1
%A A123043 _Jonathan Vos Post_, Sep 24 2006
%E A123043 More terms from _Alois P. Heinz_, Aug 12 2015