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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

%I

%S 1,2,4,7,13,14,16,19,25,26,28,31,43,55,67,70,71,72,73,74,76,77,79,82,

%T 83,84,85,86,88,89,91,94,95,96,97,98,100,101,103,106,112,113,115,118,

%U 124,125,127,130,142,154,166,241,253,265,310,311,313,316,322,323

%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 See A194368.

%H G. C. Greubel, <a href="/A194422/b194422.txt">Table of n, a(n) for n = 1..2687</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 1,2

%A _Clark Kimberling_, Aug 24 2011

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Last modified January 16 19:48 EST 2022. Contains 350376 sequences. (Running on oeis4.)