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%I #12 Jun 13 2016 04:07:38
%S 97,277,761,1511,1753,2081,3221,3643,6197,7517,7841,8263,10067,10399,
%T 10903,16903,25639,32771,32833,33013,33647,33889,35059,36137,39019,
%U 40577,40819,48563,49639,57383,59083,59567,60317,61129,62207,63199,66383,66889,100003
%N Prime sums of 4 positive 5th powers.
%C Primes in the sumset {A000584 + A000584 + A000584 + A000584}.
%C There must be an odd number of odd terms in the sum, either one even and 3 odd terms (as with 1^5 + 1^5 + 2^5 + 3^5 and 761 = 2^5 + 3^5 + 3^5 + 3^5) or three even terms and one odd term (as with 97 = 1^5 + 2^5 + 2^5 + 2^5 and 3221 = 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 Giovanni Resta, <a href="/A123033/b123033.txt">Table of n, a(n) for n = 1..10000</a>
%F A000040 INTERSECTION A003349.
%e a(1) = 97 = 1^5 + 2^5 + 2^5 + 2^5.
%e a(2) = 277 = 1^5 + 1^5 + 2^5 + 3^5.
%e a(3) = 761 = 2^5 + 3^5 + 3^5 + 3^5.
%e a(7) = 3221 = 2^5 + 2^5 + 2^5 + 5^5.
%t 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, 4}]; Select[a, PrimeQ] (* _Giovanni Resta_, Jun 13 2016 *)
%Y Cf. A000040, A000584, A003336, A003347, A003349.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 24 2006
%E More terms from _Alois P. Heinz_, Aug 12 2015
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