A374094 a(n) is the smallest nonnegative integer k where there are exactly n solutions to x^2 + x*y + y^2 = k with 0 < x < y.
0, 7, 91, 637, 1729, 31213, 12103, 405769, 53599, 157339, 593047
Offset: 0
Programs
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Maple
N:= 10^6: V:= Array(0..N): for x from 1 to floor(sqrt(N/3)) do for y from x+1 do v:= x^2 + x*y + y^2; if v > N then break fi; V[v]:= V[v]+1; od od: W:= Array(0..10); for i from 1 to N while count < 11 do v:= V[i]; if W[v] = 0 then W[v]:= i; count:= count+1 fi od: 0, seq(W[i],i=1..10); # Robert Israel, Jun 28 2024 -
Python
from itertools import count from sympy.abc import x,y from sympy.solvers.diophantine.diophantine import diop_quadratic def A374094(n): return next(m for m in count(0) if sum(1 for d in diop_quadratic(x*(x+y)+y**2-m) if 0
Formula
a(n) <= 13 * 7^(n-1).
Comments