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Least numbers k such that A088534(k) is nondecreasing.
2

%I #27 Sep 19 2019 03:25:44

%S 0,1,3,4,7,9,12,13,16,19,21,25,27,28,31,36,37,39,43,48,49,91,133,147,

%T 169,196,217,247,259,273,301,343,361,364,399,403,427,441,469,481,507,

%U 511,532,553,559,588,589,637,931,1183,1519,1729,2821,3367

%N Least numbers k such that A088534(k) is nondecreasing.

%C Least squared radius of a circle around a grid point of the hexagonal lattice such that the number of grid points on this circle is not smaller than the number of grid points on any circle around a grid point of the hexagonal lattice with smaller radius. a(1) = 0 by convention.

%H Hugo Pfoertner, <a href="/A326421/b326421.txt">Table of n, a(n) for n = 1..163</a>

%o (PARI) \\ after M. F. Hasler's A088534(n,d)

%o r2=0;for(k=0,3500,my(a088534=sum(x=0, sqrt(k\3), sum(y=max(x, sqrtint(k-x^2)\2), sqrtint(k-2*x^2), x^2+x*y+y^2==k)));if(a088534>=r2,r2=a088534;print1(k,", ")))

%Y Cf. A003136, A088534, A118886, A230655, A326311.

%K nonn

%O 1,3

%A _Hugo Pfoertner_, Sep 12 2019