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%I #15 May 29 2022 18:00:24
%S 635318657,2673,259,260,261,262,263,264,265,266,267,268,269,270,256,
%T 257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,
%U 274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292
%N a(n) is the smallest number that is the sum of n positive 4th powers in two ways.
%C This is r(n,4,2) 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 3, 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 + 240 for n >= 16.
%e a(2) = 635318657 = 59^4 + 158^4 = 133^4 + 134^4.
%e a(3) = 2673 = 2^4 + 4^4 + 7^4 = 3^4 + 6^4 + 6^4.
%Y Cf. A003824, A046881, A342902, A343078, A343079, A343082, A343086.
%K nonn
%O 2,1
%A _Sean A. Irvine_, Apr 04 2021