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 A336017 a(n) = floor(frac(Pi*n)*n), where frac denotes the fractional part. 1
 0, 0, 0, 1, 2, 3, 5, 6, 1, 2, 4, 6, 8, 10, 13, 1, 4, 6, 9, 13, 16, 20, 2, 5, 9, 13, 17, 22, 27, 3, 7, 12, 16, 22, 27, 33, 3, 8, 14, 20, 26, 33, 39, 3, 10, 16, 23, 30, 38, 45, 3, 11, 18, 26, 34, 43, 52, 4, 12, 20, 29, 38, 48, 57, 3, 13, 22, 32, 42, 53, 63, 3, 14, 24 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS It seems that the sequence can be split into consecutive short monotonically increasing subsequences. For example, the first 2^20 terms can be split into 139188 subsequences of 7 terms and 9281 subsequences of 8 terms (see commented part of Mathematica program). The distance between two consecutive terms, a(k) and a(k+1), of the same increasing subsequence is about k/7. LINKS Wikipedia, Equidistribution theorem. FORMULA a(n) = floor((Pi*n - floor(Pi*n))*n). MATHEMATICA a[n_]:=Floor[FractionalPart[Pi*n]*n]; Table[a[n], {n, 0, 100}] (* uncomment following lines to count increasing subsequences. The function MySplit[c] splits the sequence c into monotonically increasing subsequences *) (* MySplit[c_List]:=Module[{d={{c[]}}, k=1}, Do[If[c[[j]]>c[[j-1]], AppendTo[d[[k]], c[[j]]] , AppendTo[d, {c[[j]]}]; k++], {j, 2, Length[c]}]; Return[d]]; tab=Table[a[n], {n, 1, 2^20 }]; Map[Length, MySplit[tab], 1] // Tally *) PROG (PARI) a(n) = frac(Pi*n)*n\1; \\ Michel Marcus, Jul 07 2020 CROSSREFS Cf. A000796, A022844, A336018, A331008. Sequence in context: A256301 A226609 A157260 * A291486 A177870 A094872 Adjacent sequences:  A336014 A336015 A336016 * A336018 A336019 A336020 KEYWORD nonn AUTHOR Andres Cicuttin, Jul 04 2020 STATUS approved

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Last modified May 11 11:48 EDT 2021. Contains 343791 sequences. (Running on oeis4.)