|
%I #4 Feb 06 2022 21:31:12
%S 0,4,5,14,27,30,48,52,75,102,108,140,176,184,225,234,280,330,341,396,
%T 408,468,532,546,615,688,704,782,799,882,969,988,1080,1176,1197,1298,
%U 1320,1426,1536,1560,1675,1700,1820,1944,1971,2100,2233,2262,2400,2430
%N a(n) = c(n*r)*f(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 + A350526(n) = -n + f(n*x)*c(n/x), 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, A350526.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jan 04 2022
|
