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 A086520 Number of integers strictly greater than (n-sqrt(n))/2 and strictly less than (n+sqrt(n))/2. 2
 0, 0, 1, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This sequence occurs in quantum mechanics, in the context of counting certain kinds of inseparable states in an n-qubit model. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 J. S. Pratt, Universality in the entanglement structure of ferromagnets, Phys. Rev. Lett. 93, 237205 (2004) J. S. Pratt, Comments on this sequence EXAMPLE a(16) = 3 because there are three integers between 6 and 10. MAPLE a:= n-> max(0, ceil((n+sqrt(n))/2)-1-floor((n-sqrt(n))/2)): seq(a(n), n=0..120); # Alois P. Heinz, Apr 02 2014 MATHEMATICA a[n_] := If[IntegerQ[Sqrt[n]], Sum[1, {m, Ceiling[(n - Sqrt[n])/2] + 1, Floor[(n + Sqrt[n])/2] - 1}], Sum[1, {m, Ceiling[(n - Sqrt[n])/2], Floor[(n + Sqrt[n])/2]}]] CROSSREFS Sequence in context: A283431 A258594 A364215 * A012265 A339765 A268835 Adjacent sequences: A086517 A086518 A086519 * A086521 A086522 A086523 KEYWORD easy,nonn AUTHOR Jeff S. Pratt (jpratt(AT)pas.rochester.edu), Sep 10 2003 EXTENSIONS a(0)-a(1) prepended by Alois P. Heinz, Apr 02 2014 STATUS approved

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Last modified April 23 02:53 EDT 2024. Contains 371906 sequences. (Running on oeis4.)