A194397 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(14) and < > denotes fractional part.

3, 7, 11, 15, 19, 23, 27, 61, 65, 69, 73, 77, 81, 85, 89, 91, 92, 93, 95, 96, 97, 99, 100, 101, 103, 104, 105, 107, 108, 109, 111, 112, 113, 115, 116, 117, 119, 123, 127, 131, 135, 139, 143, 147, 181, 185, 189, 193, 197, 201, 205, 209, 211, 212, 213, 215

Offset: 1

Author

Clark Kimberling, Aug 23 2011

Keywords

• nonn

Comments

See A194368.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010471 (sqrt(14)), A194368, A194396, A194397.

Programs

Maple

r:= sqrt(14):
X:= 0: R:= NULL: count:= 0:
for n from 1 while count < 100 do
  X:= X + frac(1/2+n*r) - frac(n*r);
  if X > 0 then
    count:= count+1;
    R:= R, n
  fi
od:
R; # Robert Israel, Nov 25 2020

Mathematica

r = Sqrt[14]; 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, 200}];
Flatten[Position[t1, 1]]       (* A194395 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194396 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t3, 1]]       (* A194397 *)