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A194387 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(11) and < > denotes fractional part. 4
3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 25, 27, 28, 29, 31, 47, 49, 50, 51, 53, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 85, 87, 88, 89, 91, 107, 109, 110, 111, 113, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 145, 147, 148, 149, 151, 167, 169, 170 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..61.

MATHEMATICA

r = Sqrt[11]; 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]]     (* A194387 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];

Flatten[Position[t2, 1]]     (* A194388 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];

Flatten[Position[t3, 1]]     (* A194389 *)

CROSSREFS

Cf. A010468, A194368, A194388, A194389.

Sequence in context: A008521 A299489 A039231 * A039175 A048293 A039129

Adjacent sequences:  A194384 A194385 A194386 * A194388 A194389 A194390

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 23 2011

STATUS

approved

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Last modified May 22 22:13 EDT 2022. Contains 353959 sequences. (Running on oeis4.)