A194381 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(8) and < > denotes fractional part.

1, 2, 3, 7, 8, 9, 13, 14, 15, 19, 20, 21, 25, 26, 27, 31, 32, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89

Offset

1,2

Comments

See A194368.

Links

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

Mathematica

r = Sqrt[8]; c = 1/2;
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, 100}];
Flatten[Position[t1, 1]]   (* A194381 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]   (* A194382 *)
%/2  (* A194383 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];
Flatten[Position[t3, 1]]   (* A194384 *)

Crossrefs

Cf. A010466, A194368, A194382, A194383, A194384.

Sequence in context: A076682 A327224 A231624 * A047245 A070752 A039582

Adjacent sequences: A194378 A194379 A194380 * A194382 A194383 A194384

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved