A194408 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=Pi and < > denotes fractional part.

7, 13, 14, 15, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 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, 76, 77, 78, 79, 80, 81, 82

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..67.

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: A259222 A204713 A241985 * A376298 A057930 A363491

Adjacent sequences: A194405 A194406 A194407 * A194409 A194410 A194411

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved