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A194408 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=Pi and < > denotes fractional part. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A057930 A342581 A332480

Adjacent sequences:  A194405 A194406 A194407 * A194409 A194410 A194411

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified December 2 17:55 EST 2021. Contains 349445 sequences. (Running on oeis4.)