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

811538, 16578, 4225, 2676, 2677, 518, 519, 520, 521, 522, 523, 524, 525, 526, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307

Offset

3,1

Comments

This is r(n,4,3) in Alter's notation.

Links

Table of n, a(n) for n=3..52.

R. Alter, Computations and generalizations on a remark of Ramanujan, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981. See Table 8, page 192.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = n + 255 for n >= 17.

G.f.: x^3*(811538 - 1606498*x + 782607*x^2 + 10804*x^3 + 1550*x^4 - 2160*x^5 + 2160*x^6 - 255*x^14 + 255*x^15)/(1 - 2*x + x^2). - Charles R Greathouse IV, May 25 2026

Example

a(3) = 811538 = 4^4 + 23^4 + 27^4 = 7^4 + 21^4 + 28^4 = 12^4 + 17^4 + 29^4.
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.

Prog

(PARI) a(n)=if(n>16, n+255, [811538, 16578, 4225, 2676, 2677, 518, 519, 520, 521, 522, 523, 524, 525, 526][n-2]) \\ Charles R Greathouse IV, May 25 2026

Crossrefs

Cf. A085559, A123075, A342893, A343077, A343081, A343083, A343086.

Sequence in context: A178290 A083617 A386806 * A344239 A344240 A238522

Adjacent sequences: A343079 A343080 A343081 * A343083 A343084 A343085

Keyword

nonn,easy

Author

Sean A. Irvine, Apr 04 2021

Status

approved