A377372 a(n) is the smallest prime p such that the Diophantine equation x^3 + y^3 + z^3 = p^3, where 0 < x <= y <= z has exactly n positive integer solutions.

2, 19, 41, 479, 1031, 1181, 577, 2999, 10711, 29033, 24919

Offset

0,1

Links

Table of n, a(n) for n=0..10.

Example

a(3)=479, because 479^3 = 47^3 +350^3 + 406^3 = 109^3 + 293^3 + 437^3= 256^3 + 311^3 + 398^3 and no prime less than 479 has 3 solutions.

Mathematica

a = Table[SelectFirst[Table[{p, Length@Select[PowersRepresentations[p^3, 3, 3], #[[1]] > 0 &]}, {p, Prime@Range@200}], #[[2]] == k &], {k, 0, 6}]

Crossrefs

Cf. A316359, A377444.

Sequence in context: A062587 A109946 A141067 * A296251 A307554 A031911

Adjacent sequences: A377368 A377369 A377371 * A377373 A377374 A377375

Keyword

nonn,more

Author

Zhining Yang, Dec 28 2024

Status

approved