A194379 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(7) and < > denotes fractional part.

2, 14, 16, 28, 30, 32, 34, 36, 42, 44, 46, 48, 50, 62, 64, 76, 78, 80, 82, 84, 90, 92, 94, 96, 98, 110, 112, 124, 126, 128, 130, 132, 138, 140, 142, 144, 146, 158, 160, 172, 174, 176, 178, 180, 186, 188, 190, 192, 194, 206, 208, 220, 222, 224, 226, 228

Offset

1,1

Comments

All the terms are even. See A194368.

Links

Table of n, a(n) for n=1..56.

Example

r = Sqrt[7]; c = 1/2;

Mathematica

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.

Sequence in context: A105453 A199368 A121716 * A147832 A022369 A367461

Adjacent sequences: A194376 A194377 A194378 * A194380 A194381 A194382

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved