A384182 - OEIS

A384182

a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^4, where 0 < x < y < z < w has exactly n integer solutions.

6, 9, 15, 34, 20, 19, 66, 28, 36, 35, 26, 30, 355, 97, 44, 329, 151, 65, 590, 89, 48, 42, 129, 54, 70, 99, 56, 178, 580, 128, 110, 392, 107, 518, 63, 125, 90, 887, 242, 78, 100, 138, 105, 96, 235, 141, 281, 205, 326, 1094, 117, 108, 197, 860, 159, 174, 291, 134

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OFFSET

1,1

COMMENTS

a(131)>1600.

LINKS

Zhining Yang, Table of n, a(n) for n = 1..130

EXAMPLE

a(3)=15, because 15^4 = 13^3 + 21^3 + 23^3 + 30^3 = 11^3 + 16^3 + 21^3 + 33^3 = 9^3 + 11^3 + 21^3 + 34^3 and no integer less than 15 has 3 solutions.

MATHEMATICA

s=Table[{k, Length@Select[PowersRepresentations[k^4, 4, 3], 0<#[[1]]<#[[2]]<#[[3]]<#[[4]]&]}, {k, 50}]; a=Table[SelectFirst[s, #[[2]]==k&], {k, 6}][[All, 1]]

CROSSREFS

Cf. A383877.

Sequence in context: A023885 A031209 A271826 * A242183 A300564 A316050

Adjacent sequences: A384179 A384180 A384181 * A384183 A384184 A384185

KEYWORD

nonn

AUTHOR

Zhining Yang, May 21 2025

STATUS

approved