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A194374 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(5) and < > denotes fractional part. 3

%I

%S 4,8,12,16,72,76,80,84,88,144,148,152,156,160,216,220,224,228,232,288,

%T 292,296,300,304

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

%C See A194368.

%t r = Sqrt[5]; c = 1/2;

%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, 100}];

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

%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];

%t Flatten[Position[t2, 1]] (* A194374 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];

%t Flatten[Position[t3, 1]] (* A194375 *)

%Y Cf. A194368, A194375.

%K nonn,more

%O 1,1

%A _Clark Kimberling_, Aug 23 2011

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Last modified May 6 18:38 EDT 2021. Contains 343586 sequences. (Running on oeis4.)