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 A194385 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(10) and < > denotes fractional part. 3

%I

%S 6,12,18,24,30,36,228,234,240,246,252,258,264,456,462,468,474,480,486,

%T 492,684,690,696,702,708,714,720

%N Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(10) and < > denotes fractional part.

%C See A194368.

%t r = Sqrt[10]; 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, 300}];

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

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

%t Flatten[Position[t2, 1]] (* A194385 *)

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

%t Flatten[Position[t3, 1]] (* A194386 *)

%Y Cf. A010467, A194368, A194386.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 23 2011

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Last modified May 27 01:51 EDT 2022. Contains 354092 sequences. (Running on oeis4.)