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A350526 a(n) = f(n*r)*c(n/r), where f = floor, c = ceiling, and r = golden ratio (A001622). 2

%I

%S 1,6,8,18,32,36,55,60,84,112,119,152,189,198,240,250,297,348,360,416,

%T 429,490,555,570,640,714,731,810,828,912,1000,1020,1113,1210,1232,

%U 1334,1357,1464,1575,1600,1716,1742,1863,1988,2016,2146,2280,2310,2449,2480

%N a(n) = f(n*r)*c(n/r), where f = floor, c = ceiling, and r = golden ratio (A001622).

%C The golden ratio r is the unique number x such that f(n*x)*c(n/x) - c(n*x)f(n/x) = n for all n >= 1.

%F a(n) = n + A350527(n) = n + c(n*r)*f(n/r), where f = floor, c = ceiling, and r = golden ratio.

%t r = GoldenRatio; c[x_] := Ceiling[x]; f[x_] := Floor[x];

%t Table[f[n r]*c[n/r], {n, 1, 100}] (* A350526 *)

%t Table[c[n r]*f[n/r], {n, 1, 100}] (* A350527 *)

%t Table[f[n r]*c[n/r] - c[n r]*f[n/r], {n, 1, 100}] (* A000027 *)

%Y Cf. A001622, A350527.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 04 2022

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Last modified February 7 06:02 EST 2023. Contains 360112 sequences. (Running on oeis4.)