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

Author

Sean A. Irvine, Apr 04 2021

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• 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).

Crossrefs

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

Formula

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