A194378 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(7) and < > denotes fractional part.

1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 35, 37, 38, 39, 40, 41, 43, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 83, 85, 86, 87, 88, 89, 91, 97, 99, 100

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..67.

Mathematica

r = Sqrt[7]; 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]]   (* A194378 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]  (* A194379 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t3, 1]]   (* A194380 *)

Crossrefs

Cf. A194368, A194379, A194380.

Sequence in context: A108473 A298113 A026447 * A283810 A130231 A333491

Adjacent sequences: A194375 A194376 A194377 * A194379 A194380 A194381

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved