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 A194663 Number of k in [1,n] for which + > 1, where < > = fractional part and r = sqrt(2). 4
 0, 0, 2, 0, 3, 0, 1, 0, 4, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, 0, 1, 0, 4, 0, 14, 0, 14, 0, 14, 0, 11, 0, 4, 0, 8, 0, 18, 0, 14, 0, 5, 0, 10, 0, 22, 0, 17, 0, 6, 0, 13, 0, 30, 0, 31, 0, 31, 0, 31, 0, 31, 0, 31, 0, 25, 0, 12, 0, 19, 0, 37, 0, 37, 0, 31, 0, 22, 0, 41, 0, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 MATHEMATICA r = Sqrt[2]; z = 13; p[x_] := FractionalPart[x]; f[x_] := Floor[x]; w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k] Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]] TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]] s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194663 *) Table[s[n], {n, 1, 100}] h[n_, k_] := f[p[n*r] + p[k*r]] Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]    (* A194664 *) TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]] t[n_] := Sum[h[n, k], {k, 1, n}] Table[t[n], {n, 1, 100}]    (* A194665 *) CROSSREFS Sequence in context: A341980 A218031 A135523 * A135685 A164658 A079067 Adjacent sequences:  A194660 A194661 A194662 * A194664 A194665 A194666 KEYWORD nonn AUTHOR Clark Kimberling, Sep 01 2011 STATUS approved

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Last modified June 19 03:06 EDT 2021. Contains 345125 sequences. (Running on oeis4.)