A194410 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=Pi and < > denotes fractional part.

1, 2, 3, 4, 5, 9, 10, 11, 17, 95, 101, 102, 103, 107, 108, 109, 110, 111, 115, 116, 117, 123, 215, 221, 222, 223, 229, 335

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..28.

Mathematica

r = Pi; 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]]         (* A194408 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 1500}];
Flatten[Position[t2, 1]]         (* A194409 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 1500}];
Flatten[Position[t3, 1]]         (* A194410 *)

Crossrefs

Cf. A194368.

Sequence in context: A118872 A046029 A303600 * A361125 A081869 A246397

Adjacent sequences: A194407 A194408 A194409 * A194411 A194412 A194413

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved