A194465 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) < 0, where r=sqrt(2) and c=sqrt(1/2), and < > denotes fractional part.

1, 2, 4, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 21, 24, 25, 26, 28, 31, 38, 41, 42, 43, 45, 48, 49, 50, 52, 53, 54, 55, 56, 57, 59, 60, 62, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97, 98

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..68.

Mathematica

r = Sqrt[2]; c = 1/r;
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]]    (* A184465 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]    (* A184466 *)

Crossrefs

Cf. A194368.

Sequence in context: A121619 A167500 A010377 * A352246 A359585 A035261

Adjacent sequences: A194462 A194463 A194464 * A194466 A194467 A194468

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved