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A194423 Numbers m such that Sum_{k=1..m} (<2/3 + k*r> - <k*r>) = 0, where r=sqrt(2) and < > denotes fractional part. 5

%I

%S 3,6,9,12,15,18,21,24,27,30,33,36,42,45,48,54,57,60,66,69,75,78,81,87,

%T 90,93,99,102,105,108,111,114,117,120,123,126,129,132,135,141,144,147,

%U 153,156,159,165,168,171,183,195,240,243,246,252,255,258,264

%N Numbers m such that Sum_{k=1..m} (<2/3 + k*r> - <k*r>) = 0, where r=sqrt(2) and < > denotes fractional part.

%C Every term is divisible by 3; see A194368.

%H G. C. Greubel, <a href="/A194423/b194423.txt">Table of n, a(n) for n = 1..2043</a>

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

%t x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]

%t y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]

%t t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 300}];

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

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

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

%t %/3 (* A194424 *)

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

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

%Y Cf. A194368.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 24 2011

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Last modified November 29 14:08 EST 2021. Contains 349416 sequences. (Running on oeis4.)