A327796 Values of x in the n solutions corresponding to the least number A300419(n) expressible in exactly n ways as x^2 + x*y + y^2 with x >= y >= 1, with x written as triangle T(n,k), k <= n. y is given in A327797.

1, 6, 9, 17, 21, 23, 25, 32, 37, 40, 91, 107, 118, 143, 154, 66, 77, 89, 94, 98, 109, 392, 455, 507, 513, 552, 560, 595, 145, 163, 173, 177, 197, 207, 218, 230, 233, 255, 273, 310, 325, 335, 357, 378, 390, 462, 498, 539, 561, 623, 658, 686, 711, 717, 763

Offset: 1

Author

Hugo Pfoertner, Sep 25 2019

Keywords

• nonn
• tabl

Comments

A combined table for the solutions corresponding to A300419(n) was provided by Robert G. Wilson v as a text file, see link.

Examples

			The triangle begins
    1,
    6,   9,
   17,  21,  23,
   25,  32,  37,  40,
   91, 107, 118, 143, 154,
   66,  77,  89,  94,  98, 109,
  392, 455, 507, 513, 552, 560, 595,
  145, 163, 173, 177, 197, 207, 218, 230
.
T(3,1)=17, T(3,2)=21, T(3,3)=23 because
A300419(3) = 637 corresponds to the 3 solutions
637 = 17^2 + 17*12 + 12^2 = 21^2 + 21*7 + 7^2 = 23^2 + 23*4 + 4^2, using the y-values 12, 7, 4 from A327797.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..171, rows 1..18 of triangle, flattened
• Robert G. Wilson v, Solutions of a(n) for n <= 16

Crossrefs

Cf. A300419, A327797.