OFFSET
1,1
COMMENTS
There must be an odd number of odd terms in the sum, either one even and 5 odd terms (as with 37 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 and 521 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5), three even and 3 odd terms (as with 1091 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 4^5) or five even terms and one odd term (as with 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 4^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 37 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5.
a(2) = 521 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5.
a(3) = 1091 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 4^5.
a(4) = 1153 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 4^5.
MATHEMATICA
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, 6}]; Select[a, PrimeQ] (* Giovanni Resta, Jun 13 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Sep 24 2006
EXTENSIONS
More terms from Max Alekseyev, Sep 24 2011
STATUS
approved