A343083 a(n) is the smallest number that is the sum of n positive 5th powers in three ways.

13124675, 696467, 84457, 52417, 52418, 8194, 8195, 8196, 8197, 8198, 8199, 8200, 8201, 8202, 8203, 8204, 7796, 7797, 7798, 7799, 7800, 7801, 7802, 7585, 7586, 7587, 7533, 7534, 7535, 7536, 7537, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 4150, 4151, 4152, 4153, 4154, 4155, 4156, 4157, 2112

Offset

5,1

Comments

This is r(n,5,3) in Alter's notation.

Links

Table of n, a(n) for n=5..66.

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 9, page 193.

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

Formula

a(n) = n + 2046 for n >= 66.

Example

a(5) = 13124675 = 1^5 + 9^5 + 10^5 + 20^5 + 25^5 = 2^5 + 5^5 + 12^5 +23^5 + 23^5 = 16^5 + 19^5 + 20^5 + 20^5 + 20^5.
a(6) = 696467 = 1^5 + 6^5 + 8^5 + 9^5 + 9^5 + 14^5 = 3^5 + 3^5 + 7^5 + 9^5 + 12^5 + 13^5 = 4^5 + 4^5 + 4^5 + 11^5 + 11^5 + 13^5.

Crossrefs

Cf. A342895, A343077, A343080, A343081, A343082.

Sequence in context: A048937 A257269 A283274 * A342687 A342688 A206061

Adjacent sequences: A343080 A343081 A343082 * A343084 A343085 A343086

Keyword

nonn

Author

Sean A. Irvine, Apr 04 2021

Status

approved