A194401 - OEIS

A194401

Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=(1+sqrt(5))/2 and < > denotes fractional part.

1, 3, 9, 11, 17, 19, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 43, 45, 51, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 71, 77, 79, 85, 87, 111, 113, 119, 121, 145, 147, 153, 155, 161, 163, 165, 166, 167, 168, 169, 171, 173, 174, 175, 176, 177

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..61.

MATHEMATICA

r = GoldenRatio; 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}];