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A194397
Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(14) and < > denotes fractional part.
4
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
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 23 2011
STATUS
approved