A194373 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(3) and < > denotes fractional part.

3, 7, 11, 29, 33, 37, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 59, 63, 67, 85, 89, 93, 97, 99, 100, 101, 103, 104, 105, 107, 108, 109, 111, 115, 119, 123, 141, 145, 149, 153, 155, 156, 157, 159, 160, 161, 163, 164, 165, 167, 171, 175, 179, 197

Offset: 1

Author

Clark Kimberling, Aug 23 2011

Keywords

• nonn

Comments

See A194368.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A194368, A194371.

Programs

Mathematica

r = Sqrt[3]; 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, 100}];
Flatten[Position[t1, 1]]  (* A194371 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t2, 1]] (* A194372 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194373 *)

PARI

isok(n) = sum(k=1, n, frac(1/2+k*sqrt(3)) - frac(k*sqrt(3))) > 0; \\ Michel Marcus, Sep 10 2018