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A194422 Numbers m such that Sum_{k=1..m} (<2/3 + k*r> - <k*r>) < 0, where r=sqrt(2) and < > denotes fractional part. 5
1, 2, 4, 7, 13, 14, 16, 19, 25, 26, 28, 31, 43, 55, 67, 70, 71, 72, 73, 74, 76, 77, 79, 82, 83, 84, 85, 86, 88, 89, 91, 94, 95, 96, 97, 98, 100, 101, 103, 106, 112, 113, 115, 118, 124, 125, 127, 130, 142, 154, 166, 241, 253, 265, 310, 311, 313, 316, 322, 323 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194368.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..2687

MATHEMATICA

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

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, 300}];

Flatten[Position[t1, 1]]         (* A194422 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];

Flatten[Position[t2, 1]]         (* A194423 *)

%/3                              (* A194424 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];

Flatten[Position[t3, 1]]         (* A194425 *)

CROSSREFS

Cf. A194368.

Sequence in context: A217595 A280028 A094271 * A177101 A018414 A002152

Adjacent sequences:  A194419 A194420 A194421 * A194423 A194424 A194425

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)