A194377 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(6) and < > denotes fractional part.

1, 3, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 45, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 83, 85, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset

1,2

Comments

See A194368. Although a(n)=A007957(n) for n = 1..70, the number 208, for example, is here but not A007957.

Links

Table of n, a(n) for n=1..76.

Mathematica

r = Sqrt[6]; 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, 500}];
Flatten[Position[t1, 1]]   (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]]   (* A194376 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]   (* A194377 *)

Prog

(PARI) is(n)=my(r=sqrt(6), f=x->x-x\1); sum(k=1, n, f(1/2+k*r)-f(k*r))>0 \\ Charles R Greathouse IV, Jul 25 2012

Crossrefs

Cf. A007957, A194368, A194376.

Sequence in context: A249494 A047747 A007957 * A344449 A258432 A344000

Adjacent sequences: A194374 A194375 A194376 * A194378 A194379 A194380

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved