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A343082 a(n) is the smallest number that is the sum of n positive 4th powers in three ways.

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%I A343082 #9 Apr 10 2021 09:19:58
%S A343082 811538,16578,4225,2676,2677,518,519,520,521,522,523,524,525,526,272,
%T A343082 273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,
%U A343082 290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307
%N A343082 a(n) is the smallest number that is the sum of n positive 4th powers in three ways.
%C A343082 This is r(n,4,3) in Alter's notation.
%H A343082 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 8, page 192.
%H A343082 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A343082 a(n) = n + 255 for n >= 17.
%e A343082 a(3) = 811538 = 4^4 + 23^4 + 27^4 = 7^4 + 21^4 + 28^4 = 12^4 + 17^4 + 29^4.
%e A343082 a(4) = 16578 = 1^4 + 2^4 + 9^4 + 10^4 = 2^4 + 5^4 + 6^4 + 11^4 = 3^4 + 7^4 + 8^4 + 10^4.
%Y A343082 Cf. A085559, A123075, A342893, A343077, A343081, A343083, A343086.
%K A343082 nonn
%O A343082 3,1
%A A343082 _Sean A. Irvine_, Apr 04 2021