A194376 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(6) and < > denotes fractional part.

2, 4, 6, 8, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 198, 200, 202, 204, 206, 218, 220, 222, 224, 226, 238, 240, 242, 244, 246, 258, 260, 262, 264, 266, 278, 280, 282, 284, 286, 396, 398, 400

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..52.

Mathematica

r = Sqrt[6]; c = 1/2;
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, 500}];
Flatten[Position[t1, 1]]   (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]]   (* A194376 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]   (* A194377 *)

Crossrefs

Cf. A194368, A194377.

Sequence in context: A352546 A179082 A341869 * A062897 A014263 A169906

Adjacent sequences: A194373 A194374 A194375 * A194377 A194378 A194379

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved