A194397 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <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

1,1

Comments

See A194368.

Links

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

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 *)

Crossrefs

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

Sequence in context: A131098 A334228 A118894 * A330213 A039957 A217332

Adjacent sequences: A194394 A194395 A194396 * A194398 A194399 A194400

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved