A343077 a(n) is the smallest number that is the sum of n positive 4th powers in two ways.

635318657, 2673, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292

Offset

2,1

Comments

This is r(n,4,2) in Alter's notation.

Links

Table of n, a(n) for n=2..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 3, page 190.

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

Formula

a(n) = n + 240 for n >= 16.

Example

a(2) = 635318657 = 59^4 + 158^4 = 133^4 + 134^4.
a(3) = 2673 = 2^4 + 4^4 + 7^4 = 3^4 + 6^4 + 6^4.

Prog

(PARI) a(n)=if(n>15, n+240, [635318657, 2673, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270][n-1]) \\ Charles R Greathouse IV, May 16 2026

Crossrefs

Cf. A003824, A046881, A342902, A343078, A343079, A343082, A343086.

Sequence in context: A383798 A251498 A233848 * A374579 A360306 A018786

Adjacent sequences: A343074 A343075 A343076 * A343078 A343079 A343080

Keyword

nonn,easy

Author

Sean A. Irvine, Apr 04 2021

Status

approved