

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.


5



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
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OFFSET

1,2


COMMENTS



LINKS



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}];
Flatten[Position[t1, 1]] (* A194401 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]] (* A194402 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]] (* A194404 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



