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A194421 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) > 0, where r=sqrt(5) and < > denotes fractional part. 4
1, 2, 7, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 79, 82, 83, 85, 86, 87 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194368.

LINKS

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

MATHEMATICA

r = Sqrt[5]; 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, 1000}];

Flatten[Position[t1, 1]]         (* A194419 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 700}];

Flatten[Position[t2, 1]]         (* A194420 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];

Flatten[Position[t3, 1]]         (* A194421 *)

CROSSREFS

Cf. A194368.

Sequence in context: A319932 A236243 A024831 * A043357 A023730 A045281

Adjacent sequences:  A194418 A194419 A194420 * A194422 A194423 A194424

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified December 4 08:36 EST 2021. Contains 349480 sequences. (Running on oeis4.)