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%I #9 Apr 10 2021 09:19:49
%S 13124675,696467,84457,52417,52418,8194,8195,8196,8197,8198,8199,8200,
%T 8201,8202,8203,8204,7796,7797,7798,7799,7800,7801,7802,7585,7586,
%U 7587,7533,7534,7535,7536,7537,4128,4129,4130,4131,4132,4133,4134,4135,4136,4137,4138,4139,4140,4141,4142,4143,4144,4145,4146,4147,4148,4149,4150,4151,4152,4153,4154,4155,4156,4157,2112
%N a(n) is the smallest number that is the sum of n positive 5th powers in three ways.
%C This is r(n,5,3) in Alter's notation.
%H R. Alter, <a href="https://doi.org/10.1007/BFb0096461">Computations and generalizations on a remark of Ramanujan</a>, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981. See Table 9, page 193.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = n + 2046 for n >= 66.
%e a(5) = 13124675 = 1^5 + 9^5 + 10^5 + 20^5 + 25^5 = 2^5 + 5^5 + 12^5 +23^5 + 23^5 = 16^5 + 19^5 + 20^5 + 20^5 + 20^5.
%e a(6) = 696467 = 1^5 + 6^5 + 8^5 + 9^5 + 9^5 + 14^5 = 3^5 + 3^5 + 7^5 + 9^5 + 12^5 + 13^5 = 4^5 + 4^5 + 4^5 + 11^5 + 11^5 + 13^5.
%Y Cf. A342895, A343077, A343080, A343081, A343082.
%K nonn
%O 5,1
%A _Sean A. Irvine_, Apr 04 2021