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%I #10 Feb 16 2022 10:27:27
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,26,27,28,
%T 29,31,32,33,34,36,37,38,39,41,42,44,46,47,49,50,51,52,54,55,56,57,59,
%U 60,61,62,64,65,67,68,69,72,73,74,77,78,79,82,83,84,86,87,88,91,92,95,96
%N Numbers not of the form [p^c] + [q^c] + [r^c] + [s^c] + [t^c] where p, q, r, s, and t are prime, c = 41/20 = 2.05, and [...] is the floor function.
%C 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.
%C 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
%H Charles R Greathouse IV, <a href="/A320249/b320249.txt">Table of n, a(n) for n = 1..1058</a>
%H Min Zhang and Jinjiang Li, <a href="https://arxiv.org/abs/1809.04591">On a Diophantine equation with five prime variables</a>, arXiv:1809.04591 [math.NT], 2018.
%e Missing:
%e 20 = [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05]
%e 25 = [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05] + [3^2.05]
%e 30 = [2^2.05] + [2^2.05] + [2^2.05] + [3^2.05] + [3^2.05]
%e 35 = [2^2.05] + [2^2.05] + [3^2.05] + [3^2.05] + [3^2.05]
%e 40 = [2^2.05] + [3^2.05] + [3^2.05] + [3^2.05] + [3^2.05]
%e 43 = [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05] + [5^2.05]
%e 45 = [3^2.05] + [3^2.05] + [3^2.05] + [3^2.05] + [3^2.05]
%K nonn,fini
%O 1,2
%A _Charles R Greathouse IV_, Oct 08 2018
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