A194422 Numbers m such that Sum_{k=1..m} (<2/3 + k*r> - ) < 0, where r=sqrt(2) and < > denotes fractional part.

1, 2, 4, 7, 13, 14, 16, 19, 25, 26, 28, 31, 43, 55, 67, 70, 71, 72, 73, 74, 76, 77, 79, 82, 83, 84, 85, 86, 88, 89, 91, 94, 95, 96, 97, 98, 100, 101, 103, 106, 112, 113, 115, 118, 124, 125, 127, 130, 142, 154, 166, 241, 253, 265, 310, 311, 313, 316, 322, 323

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..2687

Crossrefs

Cf. A194368.

Programs

Mathematica

r = Sqrt[2]; c = 2/3;
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, 300}];
Flatten[Position[t1, 1]]         (* A194422 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]         (* A194423 *)
%/3                              (* A194424 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t3, 1]]         (* A194425 *)