A194415 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) < 0, where r=sqrt(3) and < > denotes fractional part.

1, 2, 4, 5, 8, 16, 17, 19, 20, 23, 31, 32, 34, 35, 38, 46, 47, 49, 50, 53, 56, 57, 58, 59, 60, 61, 62, 64, 65, 68, 71, 72, 73, 74, 75, 76, 77, 79, 80, 83, 86, 87, 88, 89, 90, 91, 92, 94, 95, 98, 101, 102, 103, 104, 105, 106, 107, 109, 110, 112, 113, 114, 115, 116

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..64.

Mathematica

r = Sqrt[3]; c = 1/3;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 150}];
Flatten[Position[t1, 1]]           (* A194415 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]           (* A194416 *)
%/3                                (* A194417 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 500}];
Flatten[Position[t3, 1]]           (* A194418 *)

Crossrefs

Cf. A002194, A194368, A194416, A194417, A194418.

Sequence in context: A240075 A272229 A229083 * A364779 A293536 A274796

Adjacent sequences: A194412 A194413 A194414 * A194416 A194417 A194418

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved