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%I #10 Apr 10 2021 02:48:31
%S 1375298099,51445,4097,4098,4099,4100,4101,4102,4103,4104,4105,4106,
%T 4107,4108,4109,4110,4111,4112,4113,4114,4115,4116,4117,4118,4119,
%U 4120,4121,4122,4123,4124,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067
%N a(n) is the smallest number that is the sum of n positive 5th powers in two ways.
%C This is r(n,5,2) 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 4, page 190.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = n + 1023 for n >= 33.
%e a(3) = 1375298099 = 3^5 + 54^5 + 62^5 = 24^5 + 28^5 + 67^5.
%e a(4) = 51445 = 4^5 + 7^5 + 7^5 + 7^5 = 5^5 + 6^5 + 6^5 + 8^5.
%Y Cf. A230563, A342902, A343077, A343079, A343083.
%K nonn
%O 3,1
%A _Sean A. Irvine_, Apr 04 2021