A194406 Numbers m such that Sum_{k=1..m} (<1/2 + k*e> - <k*e>) = 0 where < > denotes fractional part.

2, 4, 6, 8, 12, 26, 30, 32, 34, 36, 38, 40, 44, 58, 62, 64, 66, 68, 70, 74, 78, 80, 82, 84, 86, 90, 94, 96, 98, 100, 102, 106, 110, 112, 114, 116, 118, 122, 126, 128, 130, 132, 134, 138, 152, 156, 158, 160, 162, 164, 166, 170, 184, 188, 190, 192, 194, 196

Offset

1,1

Comments

Every term is even; see A194368.

Links

Table of n, a(n) for n=1..58.

Mathematica

r = E; 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]]       (* A194405 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194406 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]       (* A194407 *)

Crossrefs

Cf. A194368.

Sequence in context: A001217 A131885 A173941 * A371164 A087443 A059901

Adjacent sequences: A194403 A194404 A194405 * A194407 A194408 A194409

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved