A384439 a(n) is the smallest prime p such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = p^3, where 0 < x < y < z < w has exactly n positive integer solutions.
23, 13, 59, 79, 97, 139, 163, 223, 151, 283, 251, 257, 263, 277, 227, 463, 271, 373, 587, 457, 641, 461, 499, 389, 503, 683, 761, 673, 509, 523, 709, 631, 757, 619, 571, 691, 929, 727
Offset: 1
Examples
a(3)=59, because 59^3 = 13^3 + 21^3 + 41^3 + 50^3 = 14^3 + 19^3 + 44^3 + 48^3 = 21^3 + 23^3 + 26^3 + 55^3 and no prime less than 59 has 3 solutions.
Links
- Chai Wah Wu, All terms <= 4007.
Programs
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Mathematica
Table[SelectFirst[Table[{Length@Select[PowersRepresentations[p^3,4,3],#[[4]]>#[[3]]>#[[2]]>#[[1]]>0&],p},{p,Prime@Range@25}],#[[1]]==k&],{k,5}]
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