A194422 Numbers m such that Sum_{k=1..m} (<2/3 + k*r> - <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

1,2

Comments

See A194368.

Links

G. C. Greubel, Table of n, a(n) for n = 1..2687

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 *)

Crossrefs

Cf. A194368.

Sequence in context: A217595 A280028 A094271 * A177101 A018414 A002152

Adjacent sequences: A194419 A194420 A194421 * A194423 A194424 A194425

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved