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A194385 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(10) and < > denotes fractional part. 3
6, 12, 18, 24, 30, 36, 228, 234, 240, 246, 252, 258, 264, 456, 462, 468, 474, 480, 486, 492, 684, 690, 696, 702, 708, 714, 720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..27.

MATHEMATICA

r = Sqrt[10]; c = 1/2;

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]]  (* empty *)

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

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

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

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

CROSSREFS

Cf. A010467, A194368, A194386.

Sequence in context: A236240 A242650 A083263 * A043369 A028436 A184523

Adjacent sequences:  A194382 A194383 A194384 * A194386 A194387 A194388

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 23 2011

STATUS

approved

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Last modified January 27 22:13 EST 2022. Contains 350654 sequences. (Running on oeis4.)