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A194465 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) < 0, where r=sqrt(2) and c=sqrt(1/2), and < > denotes fractional part. 1
1, 2, 4, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 21, 24, 25, 26, 28, 31, 38, 41, 42, 43, 45, 48, 49, 50, 52, 53, 54, 55, 56, 57, 59, 60, 62, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97, 98 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..68.

MATHEMATICA

r = Sqrt[2]; c = 1/r;

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]]    (* A184465 *)

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

Flatten[Position[t3, 1]]    (* A184466 *)

CROSSREFS

Cf. A194368.

Sequence in context: A121619 A167500 A010377 * A035261 A047351 A242937

Adjacent sequences:  A194462 A194463 A194464 * A194466 A194467 A194468

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified October 18 22:48 EDT 2021. Contains 348070 sequences. (Running on oeis4.)