A194378 - OEIS

A194378

Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(7) and < > denotes fractional part.

1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 35, 37, 38, 39, 40, 41, 43, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 83, 85, 86, 87, 88, 89, 91, 97, 99, 100

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OFFSET

1,2

COMMENTS

See A194368.

LINKS

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

MATHEMATICA

r = Sqrt[7]; 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, 100}];