A194411 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) < 0, where r=sqrt(2) and < > denotes fractional part.

2, 14, 26, 38, 41, 43, 44, 50, 53, 55, 56, 62, 65, 67, 68, 70, 71, 72, 73, 74, 77, 79, 80, 82, 83, 84, 85, 86, 89, 91, 92, 94, 95, 96, 97, 98, 101, 113, 125, 137, 140, 142, 143, 149, 152, 154, 155, 161, 164, 166, 167, 212, 224, 236, 239, 241, 242, 248, 251

Offset

1,1

Comments

See A194368.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Mathematica

r = Sqrt[2]; c = 1/3;
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]]         (* A194411 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]]         (* A194412 *)
%/3                              (* A194413 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 150}];
Flatten[Position[t3, 1]]         (* A194414 *)

Crossrefs

Cf. A002193, A194368, A194412, A194413, A194414.

Sequence in context: A285990 A174594 A051222 * A017545 A280268 A109080

Adjacent sequences: A194408 A194409 A194410 * A194412 A194413 A194414

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved