A194386 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(10) and < > denotes fractional part.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..69.

Mathematica

r = Sqrt[10]; 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, 300}];
Flatten[Position[t1, 1]]   (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]]     (* A194385 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]     (* A194386 *)

Crossrefs

Cf. A010467, A194368, A194385.

Sequence in context: A108120 A108586 A184522 * A187390 A039215 A047253

Adjacent sequences: A194383 A194384 A194385 * A194387 A194388 A194389

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved