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a(n) = floor(r*floor(r*n)), where r = (2 + sqrt(5))/2.
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%I #5 Feb 16 2021 01:08:38

%S 4,8,12,16,21,25,29,33,40,44,48,52,57,61,65,69,76,80,84,88,93,97,101,

%T 105,110,116,120,124,129,133,137,141,146,152,156,160,165,169,173,177,

%U 182,186,192,196,201,205,209,213,218,222,228,232,237,241,245,249

%N a(n) = floor(r*floor(r*n)), where r = (2 + sqrt(5))/2.

%C Conjecture: 1/4 < n*r^2 - a(n) < 3 for n >= 1.

%t z = 50; r = GoldenRatio + 1/2; f[x_] := Floor[r*Floor[r*x]];

%t Table[f[n], {n, 1, 120} ] (* A341254 *)

%Y Cf. A341255.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Feb 13 2021