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A194411 Numbers n such that sum{<1/3+k*r>-<k*r> : 1<=k<=n}<0, where r=sqrt(2) and < > denotes fractional part. 5
2, 14, 26, 38, 41, 43, 44, 50, 53, 55, 56, 62, 65, 67, 68, 70, 71, 72, 73, 74, 77, 79, 80, 82, 83, 84, 85, 86, 89, 91, 92, 94, 95, 96, 97, 98, 101, 113, 125, 137, 140, 142, 143, 149, 152, 154, 155, 161, 164, 166, 167, 212, 224, 236, 239, 241, 242, 248, 251 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..59.

MATHEMATICA

r = Sqrt[2]; c = 1/3;

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]]         (* A194411 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];

Flatten[Position[t2, 1]]         (* A194412 *)

%/3                              (* A194413 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 150}];

Flatten[Position[t3, 1]]         (* A194414 *)

CROSSREFS

Cf. A194368.

Sequence in context: A109255 A174594 A051222 * A017545 A109080 A180877

Adjacent sequences:  A194408 A194409 A194410 * A194412 A194413 A194414

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified August 29 10:37 EDT 2015. Contains 261188 sequences.