A194407 Numbers m such that Sum_{k=1..m} (<1/2 + k*e> - <k*e>) > 0 where < > denotes fractional part.

3, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 31, 35, 39, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 63, 67, 81, 85, 87, 88, 89, 91, 92, 93, 95, 99, 113, 117, 119, 120, 121, 123, 124, 125, 127

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..64.

Mathematica

r = E; 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, 200}];
Flatten[Position[t1, 1]]       (* A194405 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194406 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]       (* A194407 *)

Crossrefs

Cf. A194368.

Sequence in context: A082768 A326911 A037372 * A241662 A097475 A177732

Adjacent sequences: A194404 A194405 A194406 * A194408 A194409 A194410

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved