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A194758

Number of k such that {k*log(2)} < {n*log(2)}, where { } = fractional part.

1, 1, 1, 4, 3, 2, 7, 5, 3, 10, 7, 4, 1, 11, 7, 3, 15, 10, 5, 19, 13, 7, 23, 16, 9, 2, 21, 13, 5, 26, 17, 8, 31, 21, 11, 36, 25, 14, 3, 31, 19, 7, 37, 24, 11, 43, 29, 15, 49, 34, 19, 4, 41, 25, 9, 48, 31, 14, 55, 37, 19, 62, 43, 24, 5, 51, 31, 11, 59, 38, 17, 67, 45, 23, 75

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..75.

MATHEMATICA

r = Log[2]; p[x_] := FractionalPart[x];

u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]

v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]

s[n_] := Sum[u[n, k], {k, 1, n}]

t[n_] := Sum[v[n, k], {k, 1, n}]

Table[s[n], {n, 1, 100}] (* A194758 *)