A343085 a(n) is the smallest number that is the sum of n positive cubes in four ways.

13896, 1979, 1252, 626, 470, 256, 224, 225, 226, 227, 221, 222, 223, 203, 204, 205, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205

Offset

3,1

Comments

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

Links

Table of n, a(n) for n=3..53.

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 11, page 194.

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

Formula

a(n) = n + 152 for n >= 19.

Example

a(3) = 13896 = 1^3 + 12^3 + 23^3 = 2^3 + 4^3 + 24^3 = 4^3 + 18^3 + 20^3 = 9^3 + 10^3 + 23^3.
a(4) = 1979 = 1^3 + 5^3 + 5^3 + 12^3 = 2^3 + 3^3 + 6^3 + 12^3 = 5^3 + 5^3 + 9^3 + 10^3 = 6^3 + 6^3 + 6^3 + 11^3.

Mathematica

LinearRecurrence[{2, -1}, {13896, 1979, 1252, 626, 470, 256, 224, 225, 226, 227, 221, 222, 223, 203, 204, 205, 171, 172}, 60] (* Harvey P. Dale, Aug 06 2022 *)

Prog

(PARI) a(n)=if(n>18, n+152, [13896, 1979, 1252, 626, 470, 256, 224, 225, 226, 227, 221, 222, 223, 203, 204, 205][n-2]) \\ Charles R Greathouse IV, May 26 2026

Crossrefs

Cf. A342902, A343081, A343084, A343086.

Sequence in context: A069302 A109483 A237941 * A343968 A343969 A190817

Adjacent sequences: A343082 A343083 A343084 * A343086 A343087 A343088

Keyword

nonn,easy

Author

Sean A. Irvine, Apr 04 2021

Status

approved