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 A123037 #11 Jun 13 2016 04:16:52
%S A123037 101,163,281,467,523,647,827,1031,1069,1093,1217,1249,1459,1733,1999,
%T A123037 2389,3163,3319,3467,3529,3623,3709,3803,3889,4217,4373,4397,4639,
%U A123037 4943,5209,5333,5693,5849,6263,6287,6529,6653,6833,7013,7411,7583,7907,8087,8329
%N A123037 Prime sums of 8 positive 5th powers.
%C A123037 Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584}.
%C A123037 There must be an odd number of odd terms in the sum, either one even and seven odd (as with 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 and 523 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5), three even and 5 odd terms (as with 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5), five even and 3 odd terms (as with 647 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5) or seven even terms and one odd term (as with 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.
%H A123037 Giovanni Resta, <a href="/A123037/b123037.txt">Table of n, a(n) for n = 1..10000</a>
%F A123037 A000040 INTERSECTION A003353.
%e A123037 a(1) = 101 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5.
%e A123037 a(2) = 163 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
%e A123037 a(3) = 281 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5.
%e A123037 a(4) = 467 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5.
%e A123037 a(5) = 523 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5.
%e A123037 a(6) = 647 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5.
%t A123037 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, 8}]; Select[a, PrimeQ] (* _Giovanni Resta_, Jun 13 2016 *)
%Y A123037 Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353.
%K A123037 easy,nonn
%O A123037 1,1
%A A123037 _Jonathan Vos Post_, Sep 24 2006
%E A123037 More terms from _Alois P. Heinz_, Aug 12 2015