A194373 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <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

1,1

Comments

See A194368.

Links

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

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 *)

Prog

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

Crossrefs

Cf. A194368, A194371.

Sequence in context: A066674 A125878 A126112 * A156210 A343718 A264803

Adjacent sequences: A194370 A194371 A194372 * A194374 A194375 A194376

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved