A194420 - OEIS

%I #8 Feb 14 2021 21:39:47

%S 3,6,9,12,21,42,60,63,72,75,78,81,84,93,114,132,135,144,147,150,153,

%T 156,165,186,204,207,216,219,222,225,228,237,258,276,279,288,291,294,

%U 297,300,309,381,453,525,597,669,687,690

%N Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) = 0, where r=sqrt(5) and < > denotes fractional part.

%C Every term is divisible by 3; see A194368.

%t r = Sqrt[5]; c = 1/3;

%t x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]

%t y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]

%t t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 1000}];

%t Flatten[Position[t1, 1]]         (* A194419 *)

%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 700}];

%t Flatten[Position[t2, 1]]         (* A194420 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];

%t Flatten[Position[t3, 1]]         (* A194421 *)

%Y Cf. A194368.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 24 2011