OFFSET
1,1
COMMENTS
Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584}. There must be an odd number of odd terms in the sum, either one even and eleven odd (as with 11 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 and 769 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 3^5), three even and nine odd (as with 347 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 3^5), five even and seven odd (as with 167 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 and 409 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5), seven even and 5 odd terms (as with 229 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5), nine even and 3 odd terms (as with 161341 = 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 11^5) or eleven even terms and one odd term (as with 353 = 1^ 5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.
LINKS
Matthew House, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 43 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5.
a(2) = 167 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
a(3) = 229 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
a(4) = 347 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 3^5.
a(5) = 353 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
a(6) = 409 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5.
a(7) = 769 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 3^5.
MAPLE
N:= 10000: # to get all terms <= N
B:= {seq(i^5, i=1..floor(N^(1/5)))}:
B2:= select(`<=`, {seq(seq(b+c, b=B), c=B)}, N):
B4:= select(`<=`, {seq(seq(b+c, b=B2), c=B2)}, N):
B8:= select(`<=`, {seq(seq(b+c, b=B4), c=B4)}, N):
B12:= select(`<=`, {seq(seq(b+c, b=B4), c=B8)}, N):
sort(select(isprime, convert(B12, list))); # Robert Israel, Aug 10 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Sep 24 2006
EXTENSIONS
More terms from Matthew House, Aug 10 2015
STATUS
approved