A194414 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) > 0, where r=sqrt(2) and < > denotes fractional part.

1, 4, 5, 6, 7, 8, 10, 11, 13, 16, 17, 18, 19, 20, 22, 23, 25, 28, 29, 30, 31, 32, 34, 35, 37, 40, 46, 47, 49, 52, 58, 59, 61, 64, 76, 88, 100, 103, 104, 105, 106, 107, 109, 110, 112, 115, 116, 117, 118, 119, 121, 122, 124, 127, 128, 129, 130, 131, 133, 134

Offset

1,2

Comments

See A194368.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Mathematica

r = Sqrt[2]; 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, 200}];
Flatten[Position[t1, 1]]         (* A194411 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]]         (* A194412 *)
%/3                              (* A194413 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 150}];
Flatten[Position[t3, 1]]         (* A194414 *)

Crossrefs

Cf. A002193, A194368, A194411, A194412, A194413.

Sequence in context: A251392 A076597 A301592 * A182204 A343916 A367187

Adjacent sequences: A194411 A194412 A194413 * A194415 A194416 A194417

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved