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%I #20 Dec 01 2018 08:25:21
%S 2160,19568,177136,1594304,14348784,129140160,1162261440,10460353136,
%T 94143178736,847288609392,7625597484912,68630377364848,
%U 617673396283888,5559060566555504,50031545098999664,450283905890997360,4052555153018976240,36472996377170786288
%N Largest number k that is not the sum of 3 squares and a nonnegative (2n+5)-th power.
%C Subsequence of A004215.
%H Vincenzo Librandi, <a href="/A299796/b299796.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = max_{2<=i<=n+1, j>=0} {4^i*(8j+7) : 4^i*(8j+7) < 3^(2n+5)}.
%e 2160 is not the sum of 3 squares and a nonnegative 7th power, and all integers larger than 2160 can be represented as the sum of 3 squares and a nonnegative 7th power (see A297970). Thus a(1) = 2160.
%t a[n_]:= Max@Table[4^k (8 Floor[3^(2 n + 5) / 2^(2 k + 3) - 7 / 8] + 7), {k, 2, n + 1}] Table[a[n], {n, 18}] (* _XU Pingya_, Nov 30 2018 *)
%Y Cf. A004215, A022552, A297970.
%K nonn
%O 1,1
%A _XU Pingya_, Feb 19 2018