A283746 - OEIS

%I #4 Mar 17 2017 22:03:43

%S 2,1,6,11,24,3,37,16,105,50,84,29,118,207,63,152,8,241,97,330,186,419,

%T 42,275,508,131,741,364,597,220,830,453,76,686,1296,309,919,1529,542,

%U 165,1762,775,1385,398,1008,21,1618,631,2228,1241,254,1851,864,2461

%N a(n) = least m such that (n-1)/n < f(m) < n/(n+1), where f(m) = fractional part of m*(golden ratio).

%C This is column 1 of A283739; |a(n+1)-a(n)| is a Fibonacci number for n>=1.

%t g = GoldenRatio; z = 10000; t =  Table[N[FractionalPart[n*g]], {n, 1, z}];

%t r[k_] := Select[Range[z], (k - 1)/k < t[[#]] < k/(k + 1) &, 1];

%t Flatten[Table[r[k], {k, 1, 200}]]  (* A283746 *)

%Y Cf. A000045, A001622, A283739, A283745.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Mar 17 2017