A194414 Numbers m such that Sum_{k=1..m} (<1/3 + 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

Author

Clark Kimberling, Aug 24 2011

Keywords

• nonn

Comments

See A194368.

Links

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

Crossrefs

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

Programs

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 *)