OFFSET
1,2
COMMENTS
Zhang & Li prove that this sequence is finite. More generally, for any 1 < c < 11216182/5471123 = 2.0500694... except c = 2, there are only finitely many numbers not of the form [p^c] + [q^c] + [r^c] + [s^c] + [t^c] where p, q, r, s, and t are prime.
It seems that a(1058) = 15980 is the last term. If there are any further terms they are larger than 7 * 10^12. - Charles R Greathouse IV, Oct 08 2018
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..1058
Min Zhang and Jinjiang Li, On a Diophantine equation with five prime variables, arXiv:1809.04591 [math.NT], 2018.
EXAMPLE
Missing:
20 = [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05]
25 = [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05] + [3^2.05]
30 = [2^2.05] + [2^2.05] + [2^2.05] + [3^2.05] + [3^2.05]
35 = [2^2.05] + [2^2.05] + [3^2.05] + [3^2.05] + [3^2.05]
40 = [2^2.05] + [3^2.05] + [3^2.05] + [3^2.05] + [3^2.05]
43 = [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05] + [5^2.05]
45 = [3^2.05] + [3^2.05] + [3^2.05] + [3^2.05] + [3^2.05]
CROSSREFS
KEYWORD
nonn,fini
AUTHOR
Charles R Greathouse IV, Oct 08 2018
STATUS
approved